Question

1. the sides of three squares join to form a right triangle as shown. if the area of square 2 is 64 cm² and the area of square 3 is 36 cm², find the area of square 1.

Explanation:

Step1: Relate squares to Pythagoras

For a right triangle, if the sides are $a, b, c$ (hypotenuse $c$), then $a^2 + b^2 = c^2$. The area of a square with side $s$ is $s^2$, so the area of square 1 is $c^2$, square 2 is $a^2$, square 3 is $b^2$.

Step2: Substitute given areas

$\text{Area of square 1} = \text{Area of square 2} + \text{Area of square 3}$
$\text{Area of square 1} = 64 + 36$

Step3: Calculate total area

$\text{Area of square 1} = 100$

Answer:

$\boldsymbol{100}$ $\text{cm}^2$