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BECE Mathematics 2010 Paper

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Question : 31

Total: 40

X Y Z

is a right-angled triangle with length of sides as shown.

Which of the following equations gives the value of

z^2

$\;\;z^2=(x^2+y^2)$
$\;\;z^2=(x-y)$
$\;\;z^2=(y^2-y^2)$
$\;\;z^2=(x^2-y^2)$

Solution:

Concept:

By Pythagoras theorem, the square of the hypotenuse equals the sum of the squares of the other two sides.

Explanation:

The hypotenuse is the longest side, and it is opposite the right angle.

In the given triangle, the side facing the right angle is

y

, so

y

is the hypotenuse.

Thus,

y^2 = x^2 + z^2

.

Subtract

x^2

from both sides to isolate

z^2

:

z^2 = y^2 - x^2

.

Answer:

z^2 = y^2 - x^2

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