- Use Pythagoras' Theorem to calculate the length of the hypotenuse in the isosceles triangle below. Give your answer correct in exact surd form. (2 marks)
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- Using your result from part (a) above, calculate the perimeter of the shape below, correct to 1 decimal place. (2 marks)
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Right-angled Triangles, SM-Bank 052
Use Pythagoras' Theorem to calculate the perimeter of the isosceles triangle below, correct to the nearest centimetre. (3 marks)
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Show Worked Solution
\(\text{Find length of the equal sides of the triangle.}\)
\(\text{Pythagoras’ Theorem states: }c^2=a^2+b^2\)
\(\text{Let }a=5\ \text{and }b=8\)
| \(\text{Then}\ \ c^2\) | \(=5^2+8^2\) |
| \(c^2\) | \(=89\) |
| \(c\) | \(=\sqrt{89}\) |
| \(c\) | \(=9.433\dots\) |
\(\text{Perimeter}\)
\(=2\times 9.433\dots+10\)
\(=28.867\dots\approx 29\ \text{cm}\ (\text{nearest cm})\)
Right-angled Triangles, SM-Bank 051
Use Pythagoras' Theorem to calculate the perimeter of the trapezium below, correct to 1 decimal place. (3 marks)
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Show Worked Solution
\(\text{Find length of sloped side of trapezium.}\)
\(\text{Pythagoras’ Theorem states: }c^2=a^2+b^2\)
\(\text{Let }a=4\ \text{and }b=7)
| \(\text{Then}\ \ c^2\) | \(=4^2+7^2\) |
| \(c^2\) | \(=65\) |
| \(c\) | \(=\sqrt{65}\) |
| \(c\) | \(=8.062\dots\) |
\(\text{Perimeter}\)
\(=6+7+10+8.062\dots\)
\(=31.062\dots\approx 31.1\ \text{mm}\ (1\ \text{d.p.})\)
Right-angled Triangles, SM-Bank 050
Use Pythagoras' Theorem to calculate the perimeter of the rectangle below, correct to 1 decimal place. (3 marks)
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Right-angled Triangles, SM-Bank 049
- Calculate the length of the hypotenuse in the following right-angled triangle. Give your answer correct to the nearest metre. (2 marks)
- Find the perimeter of the triangle. (1 mark)
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