Question

A right triangle is formed by joiningthree squares.6 inWhat is theside length ofthe medium100 in?square?+Ee

Answer 1

x = 8 in

Step-by-step explanation

We have to find x. We know the side length of one side - which is 6 in - and we can find the side length of the hypotenuse, because we know that the figure below the triangle is a square and we're given its area. The area of a square is its side length squared:

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

Now, using the pythagorean theorem we find x:

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