Question

What is the area, in the square centimeters, of the triangle shown?

Answer 1

Solution

- The solution steps are given below:

$\begin{gathered} \text{ The hypotenuse is 24.} \\ \text{ Since this is a 45-45-90 triangle, the sides AB and BC are equal and they are:} \\ AB\sqrt{2}=AC \\ AB\sqrt{2}=24 \\ \therefore AB=\frac{24}{\sqrt{2}}=12\sqrt{2} \\ \\ \therefore\text{ The area of the triangle:} \\ A=\frac{1}{2}\times BC\times AB\text{ \lparen}\frac{1}{2}\times base\times height) \\ \\ A=\frac{1}{2}\times12\sqrt{2}\times12\sqrt{2} \\ \\ A=144 \end{gathered}$

Final Answer

The area is 144 square cm (OPTION A)