Alg 2
posted by Anna on .
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.
Find the value of x and find the new dimensions of the frame.
How do you do this?? Please show work

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 
The new dimensions of the frame are:
Lenght = 8+4 = 12 in
Width = 4+4 = 8 in