Question

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

Answer 1

- 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√(2)=AC \\ AB√(2)=24 \\ \therefore AB=(24)/(√(2))=12√(2) \\ \\ \therefore\text{ The area of the triangle:} \\ A=(1)/(2)* BC* AB\text{ \lparen}(1)/(2)* base* height) \\ \\ A=(1)/(2)*12√(2)*12√(2) \\ \\ A=144 \end{gathered}`

Final Answer

The area is 144 square cm (OPTION A)