a rectangular picture frame measures 8 inches by 4 inches. You want to triple the frame's area by adding the same distance, x, to the length and width.

Question

Find the value of x and find the new dimensions of the frame.

How do you do this?? Please show work

Answer 1

L = Lenght = 8 in

W = Width = 4 in

A = Area = L*W = 8*4 = 32 in^2

3A = 3*32 = 96 in^2

(L+x)*(W+x) = 3A

(8+x)*(4+x) = 96

4*8 + 4*x + x*8 + x*x = 96

32 + 4x + 8x + x^2 = 96

x^2 + 12x + 32 - 96 = 0

x^2 + 12x - 64 = 0

The exact solutions of this equation are:

x = 4

and

x = -16

Distance can't be negative so:

x=4

(8+4) * (4+4) = 12 * 8 = 96 in^2 = 3A

Answer 2

The new dimensions of the frame are:

Lenght = 8+4 = 12 in

Width = 4+4 = 8 in