The triangle below is isosceles.
- Use Pythagoras' Theorem to calculate the perpendicular height (\(h\)) of the triangle. (2 marks)
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- Using your answer from (a), find the area of the triangle. (2 marks)
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Show Worked Solution
a.
| \(a^2+b^2\) | \(=c^2\) |
| \(h^2+5^2\) | \(=13^2\) |
| \(h^2\) | \(=13^2-5^2\) |
| \(h^2\) | \(=144\) |
| \(h\) | \(=12\) |
\(\therefore\ \text{The perpendicular height of the triangle is }12\ \text{m}\)
| b. | \(\text{Area}\) | \(=\dfrac{1}{2}\times bh\) |
| \(=\dfrac{1}{2}\times 10\times 12\) | ||
| \(=60\ \text{m}^2\) |