Please HELP ME!!!

Question

The length of a rectangle is 3x+4 and the width is 2x+7.

A. Write an equation for the perimeter P ofthe rectangle.

B. The perimeter of the rectangle is 62 feet. What is the value of x?

C. What are the length and width of the rectangle?

Answer 1

A rectangle has four sides: top and bottom (same size) and left/right sides (same size).

Perimeter is adding all four sides together. Therefore, you have length + length + width + width

We are given that length (L) = 3x+4 and width (W) = 2x+7

a) If Perimeter (P) = L + L + W + W = 2L + 2W then

P = 2(3x+4) + 2(2x+7) Simplify

P = 6x+8 + 4x+14 Combine like terms

P = 6x+4x + 24+14

P = 10x + 22

b) If Perimeter (P) = 62 then what is x in equation a)?

P = 10x + 22

62 = 10x + 22

62 - 22 = 10x

40 = 10x

40/10 = x

4 = x

c) Find the lengths and widths.

We know the equation for length (L) = 3x+4 and we know that x= 4 so let's plug that in

L = 3x + 4

L = 3(4) + 4

L = 12 + 4

L = 16

Repeat for width.

W = 2x+7

W = 2(4) + 7

W = 8 + 7

W = 15

Check to see if 15+15+16+16 = the perimeter given (62)

15+15+16+16 = 62, yes