Question 1172184
 The width of Jennica’s small painting is 3 inches less than its length.
 A 1-inch border is put around the painting to protect the sides of her masterpiece.
 The area of the painting and the border is 108 square inches.
 What is the length and the width of Jennica’s original painting?
:
Let L = length of original painting
let w = it's width
:
write an equation for each statement
:
" The width of Jennica’s small painting is 3 inches less than its length."
w = L - 3
;
" A 1-inch border is put around the painting to protect the sides of her masterpiece."
 1 inch borders adds 2 inches to length and width
Overall dimensions: (L+2) by (w+2)
:
" The area of the painting and the border is 108 square inches."
(L+2)*(w+2) = 108
replace w with (L-3)
(L+2)*((L-3)+2) = 108
(L+2)*(L-1) = 108
FOIL
L^2 + 2L - L - 2 = 108
L^2 + L - 2 - 108 = 0
L^2 + L - 110 = 0
Factors to
(L+11)(L-10) = 0
the positive solution
L = 10 inches is the original length of the painting
the
10-3 = 7 inches is original width
:
:
Check solution with overall dimensions: 12 * 9 = 108