MATH SOLVE

7 months ago

Q:
# The length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle.

Accepted Solution

A:

Length of rectangle = 5 less than 2x width

Perimeter = 146 cm

Equations we will use...

w = width

(2w - 5) = length (l)

perimeter (p) = 2(l + w)

Substitute equation for length into equation for perimeter

p = 2(l + w)

146 = 2((2w - 5) + w) [use distributive prop.]

146 = 4w - 10 + 2w [combine like terms]

146 = 6w -10 [solve for w]

156 = 6w

w = 26 cm

Now substitute width back into the equation for length...

l = 2w - 5

l = 2(26) - 5

l = 47

Double check to make sure values added up to 146 cm

w + w + l + l = 146

26 + 26 + 47 + 47 = 146

146 = 146

Therefore, the width is 26 cm and the length is 47 cm.

Perimeter = 146 cm

Equations we will use...

w = width

(2w - 5) = length (l)

perimeter (p) = 2(l + w)

Substitute equation for length into equation for perimeter

p = 2(l + w)

146 = 2((2w - 5) + w) [use distributive prop.]

146 = 4w - 10 + 2w [combine like terms]

146 = 6w -10 [solve for w]

156 = 6w

w = 26 cm

Now substitute width back into the equation for length...

l = 2w - 5

l = 2(26) - 5

l = 47

Double check to make sure values added up to 146 cm

w + w + l + l = 146

26 + 26 + 47 + 47 = 146

146 = 146

Therefore, the width is 26 cm and the length is 47 cm.