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Rectilinear Figures, SM-Bank 045

An isosceles triangle has a base of length 4 centimetres and a perimeter of 20 centimetres.

Find the length of the equal sides.  (2 marks)

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\(8\ \text{cm}\)

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\(\text{Let the length of the equal sides be}\ x\)

\(\text{Then,}\ \ 2\times x+4\) \(=20\)
\(2x\) \(=20-4\)
\(2x\) \(=16\)
\(x\) \(=8\)

\(\therefore\ \text{The equal sides are of length }8\ \text{cm}\)

Rectilinear Figures, SM-Bank 024

A rectangle has a length of 12 cm and a width of 7 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres?  (2 marks)

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\(9.5\ \text{cm}\)

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\(\text{Perimeter of Rectangle}\)

\(=2\times 12 +2\times 7\)

\(=38\ \text{cm}\)

\(\text{Side length of square}\)

\(=\dfrac{38}{4}\)

\(=9.5\ \text{cm}\)

Rectilinear Figures, SM-Bank 022

Joyce is walking her dog around a paddock in the shape of a parallelogram.

If she walks the dog around the paddock in the morning and the afternoon, how many kilometres do they walk each day?  (2 marks)

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\(14.8\ \text{km}\)

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\(\text{Perimeter of paddock}\)

\(=2\times 1.4+2\times 2.3\)

\(=7.4\ \text{km}\)

\(\text{Total distance walked each day}\)

\(=2\times 7.4\)

\(=14.8\ \text{km}\)

Rectilinear Figures, SM-Bank 020

Tatiana is cutting a piece of material in the shape of a parallelogram for a sewing project.

The longer sides are one and two-thirds times the length of the shorter sides.

What is the perimeter of the piece of material?  (2 marks)

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\(96\ \text{cm}\)

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\(\text{Longer side}\) \(=\dfrac{5}{3}\times 18\)
  \(=30\ \text{cm}\)

 

\(\therefore\ \text{Perimeter}\) \(=2\times 18 +2\times 30\)
  \(=96\ \text{cm}\)

Rectilinear Figures, SM-Bank 019

Fumiko is laying pavers that are shaped like a parallelogram.

 
The longer sides are 3.5 times the length of the shorter sides.

What is the perimeter of one of the pavers?  (2 marks)

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\(72\ \text{cm}\)

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\(\text{Longer side}\) \(=8\times 3.5\)
  \(=28\ \text{cm}\)

 

\(\therefore\ \text{Perimeter}\) \(=2\times 8 +2\times 28\)
  \(=72\ \text{cm}\)

Rectilinear Figures, SM-Bank 017

A rectangular parking lot has a perimeter of 80 metres.

Each short side has a length of 10 metres.

What is the length of the long side?  (2 marks)

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\(30\ \text{m}\)

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\(\text{Let}\ \ d=\text{long side of parking lot}\)

\(2\times d + (2\times 10)\) \(=80\)
\(2d\) \(=80-20\)
\(2d\) \(=60\)
\(\therefore\ d\) \(=30\ \text{m}\)

Rectilinear Figures, SM-Bank 015

The length of this rectangle is one and a half times its height.
 

The perimeter of the rectangle is 40 centimetres.

What are the dimensions of the rectangle?  (2 marks)

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\(\text{Height}=8\ \text{cm}\)

\(\text{Length}=12\ \text{cm}\)

Show Worked Solution
\(\text{Let}\ \ \ x\) \(=\text{height}\)
\(\dfrac{3}{2}x\) \(=\text{length}\)
\(2\times \Big(x +\dfrac{3}{2}x\Big)\) \(= 40\)
\(2\times \Big(\dfrac{5x}{2}\Big)\) \(= 40\)
\(5x\) \(= 40\)
\(x\) \(= 8\)
\(\therefore\ \text{Height}\) \(= 8\ \text{cm}\)
\(\therefore\ \text{Length}\) \(=\dfrac{3}{2}\times 8\)
  \(=12\ \text{cm}\)

Rectilinear Figures, SM-Bank 013

Aragorn is fencing a paddock on his property. The total length of fencing he requires is 8.2 kilometres.

The length of the paddock is 2.8 kilometres.
 

 
How wide is the paddock?

Write your answer, in kilometres to one decimal place?  (2 marks)

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\(1.3\ \text{km}\)

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\(\text{Express as a perimeter equation:}\)

\(2\times 2.8 + 2x\) \(= 8.2\)
\(2x\) \(= 8.2-5.6\)
\(2x\) \(= 2.6\)
\(\therefore x\) \(=1.3\ \text{km}\)

\(\therefore\ \text{Side length is }1.3\ \text{km}\)

Rectilinear Figures, SM-Bank 010

A rectangle has a length of 25 cm and a width of 20 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres?  (2 marks)

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\(22.5\ \text{cm}\)

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\(\text{Perimeter of rectangle}\) \(= (2\times 25) + (2\times 20)\)
  \(=90\ \text{cm}\)

 

\(\therefore\ \text{Side length of square}\) \(=\dfrac{90}{4}\)
  \(=22.5\ \text{cm}\)

Rectilinear Figures, SM-Bank 006

A rectangular car park is shown below with a perimeter of 70 m.

 
 
What is the length of the short side \(\large x\)?  (2 marks)

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\(10\ \text{m}\)

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\(\text{Perimeter}\) \(=25 + 25 + x +x\)
\(70\) \(=50 + 2x\)
\(2x\) \(=70-50=20\)
\(\therefore x\) \(=10\ \text{m}\)

 

Rectilinear Figures, SM-Bank 005 MC

Andrew drew a shape as pictured below.
 

 
What is the perimeter of this shape in centimetres?

  1. \(101\)
  2. \(127\)
  3. \(148\)
  4. \(154\)
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\(D\)

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\(\text{Starting at the bottom left corner and}\)

\(\text{moving clockwise:}\)

\(\text{Perimeter}\) \(= 26 + 30 + 26 + 8 + 21 + 16 + 21 + 6\)
  \(= 154\ \text{cm}\)

\(\Rightarrow D\)

Rectilinear Figures, SM-Bank 004

Justin connects three of his restaurant tables together to make one long table.

The view from above the tables is shown below.
 

 Each table is 70 cm long and 50 cm wide.

What is the perimeter of the long table?  (2 marks)

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\(520\ \text{cm}\)

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\(\text{Perimeter}\) \(= 2\times (210 + 50)\)
  \(= 2\times 260\)
  \(= 520\ \text{cm}\)

Rectilinear Figures, SM-Bank 003 MC

The table shows the dimensions of four different rectangles in centimetres.

Rectangle Length (cm) Width (cm)
1 9 5
2 10 8
3 14 2
4 18 10

 
Which rectangle has a perimeter of 28 centimetres?

  1. Rectangle 1
  2. Rectangle 2
  3. Rectangle 3
  4. Rectangle 4
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\(A\)

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\(\text{Consider rectangle 1}\)

\(\text{Perimeter}\) \(= 2\times \text{length} + 2\times \text{width}\)
  \(= (2\times 9) + (2\times 5)\)
  \(=28\ \text{cm}\)

  
\(\therefore\ \text{Rectangle 1 has a perimeter of 28 cm.}\)

\(\Rightarrow A\)