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WAEC Mathematics 2012 Paper

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Question : 16

Total: 49

In

\triangle

XYZ, /XY/ = 8cm, /YZ/ = 10cm and /XZ/ = 6cm. Which of these relation is true?

/XY/ + /YZ/ = /XZ/
/XY/ - /YZ/ = /XZ/
/XY/² = /Y/² - /XY/²
/YZ/² = /XZ/² + /XY/²

Solution:

Concept:

Check whether the given side lengths satisfy Pythagoras' theorem.

Explanation:

In

\triangle XYZ

,

XY = 8

cm,

YZ = 10

cm, and

XZ = 6

cm.

The largest side is

YZ = 10

cm.

Apply Pythagoras' theorem:

6^2 + 8^2 = 36 + 64 = 100

.

Also

10^2 = 100

.

Thus,

YZ^2 = XZ^2 + XY^2

.

This relation is exactly option D.

Answer:

D.

YZ^2 = XZ^2 + XY^2

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