Question

A rectangle with a length of 2 w minus 6 and width of w. An equilateral triangle with side lengths of w + 8. The perimeters of a rectangle and an equilateral triangle are equal. Which expression represents the rectangle's perimeter? 2w – 6 + w Which expression represents the triangle's perimeter? What is the perimeter of both polygons?

Answer 1

See explanation

Explanation:

We have the length of the rectangle as 2w - 6 and width of the rectangle as w. The perimeter of a rectangle is given by 2(l + b) hence;

perimeter of the rectangle = 2 (2w - 6 + w) = 6w -12

For an equilateral triangle in which each side is w + 8, its perimeter is;

3(w + 8) = 3w + 24

Then the question goes further to say that the perimeter of the rectangle and equilateral triangle are equal

6w -12 = 3w + 24

6w - 3w = 24 + 12

3w = 36

w =12

Hence perimeter of rectangle = 6(12) -12 = 60

Perimeter of equilateral triangle =3(12) + 24 = 60