Question

1. The image below shows the three squares joined at their vertices to form a right triangle. What is he length of the side of the shaded triangle? 64 in 225 in neho

Answer 1

The Pythagorean Theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares of the other two sides in a right triangle.

`\begin{gathered} a^2+b^2=c^2 \\ \text{ Where c is the hypotenuse and} \\ \text{a and b are the sides of the right triangle} \end{gathered}`

Graphically

So, in this case, you have

`\begin{gathered} a^2=225in^2 \\ b^2=64in^2 \\ a^2+b^2=c^2 \\ 225in^2+64in^2=c^2 \\ 289in^2=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{289in^2}=\sqrt[]{c^2} \\ 17in=c \end{gathered}`

Therefore, the hypotenuse of the triangle or the length of the side of the shaded triangle is 17 inches.