1) A rectangle has perimeter 38 feet and an area of 78 square feet. Find the dimensions of the rectangle assuming the width is smaller than the length.

Question

L= W=

2) A rectangular canvas picture measures 9 inches by 7 inches. The canvas is mounted inside a frame of uniform width, increasing the total area covered by both canvas and frame to 120 square inches. Find the uniform width of the frame.

Answer 1

LW = 78, so L = 78/W
L+W = 19
78/W + W = 19
W^2 - 19W + 78 = 0
W=6,L=13

for the picture, if the frame has width w, then

(7+2w)(9+2w) = 120
now just solve for w.
Just by looking, I'd say that 10x12 = 120, so w=1.5