Math help for homework

Question

The length of a rectangle is 3 inches more than its width . The area of the rectangle is equal to 2 inches more than 2 times the perimeter

Answer 1

L=W+3 = length

LW=2+2L+2W = area = 2 + perimeter (perimeter = 2 times the width plus 2 times the length)

LW=2(1+L+W) L=W+3, substitute to get an equation with only one variable W

(W+3)W=2(1+W+3+W)

W²+3W=2(4+2W)=8+4W

rearrange to put in a standard quadratic for = 0

W²-W-8=0

Use the quadratic formula

W=(1/2)(1 + or - square root of 1-4(1)(-8). ignore the negative square root

=(1/2)(1+ square root of 33)

= approximately (1/2)(6.74) = 3.37

L=W+3= 3.37+3 = 6.37 Area = LW=21.47

The perimeter is 2L+2W = 2(L+W)=2(3.37+6.37)=2(9.74)=19.48 = approximately 21.47 -2

Length of the rectangle is 6.37 Width is 3.37, rounded to two decimal places.