Question

Three squares arejoined at the verticesto form a right triangle.The figure on the rightshows the areas of twoof the three squares.What could be the areaof the third square?A-36 inchesB-18 inchesC-2 inchesD-164 inches

Answer 1

According to the information given, a square has all of its sides with the same measurement.

The square of 100 square inches, can have a side of the sqrt of the area

`\begin{gathered} s=\sqrt[]{100}in^2 \\ s=10in \end{gathered}`

same happens for the other square of 64 square inches

`\begin{gathered} s=\sqrt[]{64in^2} \\ s=8in \end{gathered}`

As the figure in the middle forms a right triangle find the missing side using the pithagorean

`\begin{gathered} 10^2=8^2-x^2 \\ 10^2-8^2=x^2 \\ 100-64=x^2 \\ 36=x^2 \\ \sqrt[]{36}=x \\ 6=x \end{gathered}`

now calculate the area of the square.

`\begin{gathered} A=6in^2 \\ A=36in^2 \end{gathered}`