Question

Use the Pythagorean relationship to find the unknown area of each square

Answer 1

• (a)65

,

• (b)24

Explanation:

The Pythagorean relationship for three sides of a right triangle, a, b, and c where c is the hypotenuse (the slant side) is:

`c^2=a^2+b^2`

Part C

On the hypotenuse side: c²=90

`\begin{gathered} c^2=a^2+b^2 \\ 90=a^2+25 \\ a^2=90-25 \\ a^2=65\text{ square units} \end{gathered}`

The unknown area of the square is 65 square units.

Part D

On the hypotenuse side: c²=?

`\begin{gathered} c^2=a^2+b^2 \\ c^2=12+12 \\ c^2=24\text{ square units} \end{gathered}`

The unknown area of the square is 24 square units.