the length of a rectangle is 5 centimeters less than twice it’s width. it’s area is 63 square centimeters. find the dimensions of the rectangle

Question

you need to find the with and length and if cm or cm squared/cubed

Answer 1

length of a rectangle is 5 centimeters less than twice it’s width:

L = 2W - 5

 

area is 63 square centimeters:

A = 63

Area is length times width so:

LW = 63

 

(2W-5)(W) = 63

2W² - 5W = 63

2W² - 5W - 63 = 0

 

This quadratic can be factored by grouping.

2(-63) = -126

Factors of -126 that add to -5 are -14(9)

Replace -5W with -14W + 9W and group

 

2W² - 14W + 9W - 63 = 0

2W(W - 7) + 9(W - 7) = 0

(2W + 9)(W - 7) = 0

 

Either 2W+9=0 and W = -9/2

OR

W-7 = 0  and W = 7

 

Since the width will not be a negative, we have w = 7 cm

 

L = 2W-5 = 2(7)-5 = 9

 

The rectangle is 9 cm by 7 cm