Question

5. Determine the area of the square that would be attached to the hypotenuse of each right triangle. a) 17 cm 26 cm m ^ 2 + 15 ^ 2 = c ^ 2 7 cm 967.2 cm b)

Answer 1

Identify and Set Up

This question is a test on the understanding of the Pythagorean theorem.

It states that the square of the length of the hypothenuse of a right angled triangle is equal to a sum of the squares of the other sides.

Our approach, given the length of the other sides, is simply to find the square of the hypothenuse which is a sum of the square of the other 2 sides.

Execute

$\begin{gathered} h^2=o^2+a^2 \\ \text{ Where:} \\ h=\text{hypothenuse} \\ o=\text{Opposite side} \\ a=\text{Adjacent side} \end{gathered}$

This gives us:

a.

$h^2=17^2+26^2=965\operatorname{cm}^2$

Area of square with length as hypotenuse = 965 sq cm

b.

$h^2=7^2+15^2=274\operatorname{cm}$

Area of square with length as hypotenuse = 274 sq cm