Question

A rectangle is 6 units wide and x-8 units long. It has the same area as a triangle with the height of 7 units and a base of x-3 units and a base of x-3 units. What s the area of the rectangle

Answer 1

AREA OF A RECTANGLE IS 42 UNITS

Rectangle:                             Triangle: 
A = L * W                             A = hb / 2
A = (x-8) * 6                         A = (7(x-3)) / 2
A = 6x - 48                            A = (7x - 21) / 2

Since the problem states that both rectangle and triangle have the same area.Then:

6x - 48 = (7x - 21) / 2

1) Eliminate the denominator 2 by multiplying both sides by 2.

2 * (6x - 48) = 2 * ((7x - 21) / 2)
12 x - 96 = 7x - 21

Find x. Transfer like numbers and change their signs.

12x - 7x = 96 - 21
5x = 75
5x / 5 = 75 / 5
x = 15

Substitute x by its value:

Rectangle:                            Triangle
A = (x-8) * 6          -                A = (7(x-3)) / 2                      Areas of both Rectangle
A = (15 -8 ) * 6                       A = (7(15-3)) / 2                      and Triangle is the same.
A = 7 * 6                                  A = (7 * 12) / 2
A = 42 units                            A = 84 / 2
                                               A = 42 units