Question

I will send you a picture of the work problem and the answer choices

Answer 1

Area of a triangle (At):

`A_t=(b* h)/(2)`

In your problem:

b = b

h = a

As you have four triangles in the figure:

`A_t=4*(b* a)/(2)=2ab`

Area of a square (As):

`A_s=c^2`

The expression of the area (A) of the figure would be:

`A=2ab+c^2`
`A\text{ =(}a+b)^2`

Also, solving the quadratic expression, the equivalent would be:

`A\text{ =}a^2+2ab+b^2`

Setting two of these equal to each other and subtracting 2ab from the equation results in the Pythagorean Theorem

`\begin{gathered} 2ab+c^2\text{ =}a^2+2ab+b^2 \\ -2ab+2ab+c^2=a^2+2ab-2ab+b^2 \\ c^2=a^2+b^2 \end{gathered}`