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Area, SM-Bank 048

Jocasta is sewing a quilt in the shape of a rectangle, as shown below. She knows the length of one side, and the length of diagonal of the quilt.

  1. Calculate the length of the other side of the quilt, giving your answer in exact surd form.  (2 marks)

  2. Using your answer from (a) calculate the area of the quilt in square metres, correct to 1 decimal place?  (2 marks)


Show Answers Only

a.    \(\sqrt{2.05}\ \text{m}\)

b.    \(2.6\ \text{m}^2\ (1\ \text{d.p.})\)

Show Worked Solution

a.    \(\text{Using Pythagoras to find the shorter side:}\)

\(a^2+b^2\) \(=c^2\)
\(a^2+1.8^2\) \(=2.3^2\)
 \(a^2\) \(=2.3^2-1.8^2\)
\(a^2\) \(=2.05\)
 \(a\) \(=\sqrt{2.05}\ \text{m}\)

 

b.    \(\text{Area}\) \(=l\times b\)
    \(=1.8\times \sqrt{2.05}\)
    \(=2.577\dots\)
    \(=2.6\ \text{m}^2\ (1\ \text{d.p.})\)