Question

The figure is made up of a triangle and a rectangle it has a total area of 160 square inches AB = BC = BF = FE find the length of AB

Answer 1

8 in

Explanation:

Let the length of AB be x in:

`AB = BC = BF = FE=x \ in`

Area of the triangular part is calculated as:

`A_t=(1)/(2)bh\\\\=(1)/(2)* x * x \\\\=0.5x \ in^2`

Area go the rectangular part is calculated as:

`A=lw\\\\=x* 2x\\\\=2x^2 \ in^2`

The total area is given as 160 sq in. We equate this to the two areas to solve for x:

`A=lw+0.5bh\\\\160=2x^2+0.5x^2\\\\x^2=(160)/(2.5)=64\\\\x=8 \ in`

Hence, the length of AB is 8 in