Lina has a rectangular frame that surrounds a 4x6 inch picture. the frame has a strip of uniform width, x inches, around the outside. the area of the strip is 24 square inches.

Question

a. what is the area of the inner rectangle?

b. what is the width of the strip in inches if the area of the strip is 24 sq.inch.

Answer 1

There are several ways to find the area of the frame:

(the picture is arbitrarily in landscape format for the descriptions below)

(1) Area of 4 square corners=4x²; top and bottom strips=12x; side strips=8x. Total area: 20x+4x².

(2) Area of top and bottom strips including corners=2x(6+2x)=12x+4x²; side strips=8x. Total area: 20x+4x².

4x²+20x=24in² (given), x²+5x-6=0=(x+6)(x-1), so x=1" (the other value is negative, so is meaningless).

(a) The area of the inner rectangle is the area of the picture=4×6=24in².

(b) The width of the strip (frame)=1" (see calculations above).