In the diagram above , XZ is the diameter of the circle XZW, with center...

JAMB 2002

In the diagram above , XZ is the diameter of the circle XZW, with center O and radius 15/2 cm. If XY = 12 cm, find the area of the triangle XYZ

A. 54 cm²
B. 45 cm²
C. 27 cm²
D. 75 cm²

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Correct Answer: Option A

Explanation

Since radius = \(\frac{15}{2}\) diameter = 2 * (\(\frac{15}{2}\)) = 15cm
XYZ is a right-angled triangle (since <Y = 90º )
∴ 15\(^2\) = 12\(^2\) + (YZ)\(^2\)
225 = 144 = (YZ)\(^2\)
225 - 144 = (YZ)\(^2\)
81 = (YZ)\(^2\)
\(\sqrt{81}\) = YZ
9 = YZ
Area of ΔXYZ = \(\frac{1}{2}\)bh
(\(\frac{1}{2}\) x 9 x 12
9 x 6 = 54
= 54cm\(^2\)

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