A rectangle has a perimeter of 80 feet. Its height is 5 feet shorter than 4 times its base. What are the dimensions of this rectangle?

1 Answer
Oct 19, 2017

31 feet by 9 feet

Explanation:

Firstly, label the dimensions of the rectangle as variables.

Since the perimeter is 80 feet, all four sides must add up to 80

Let the height #=h#
and the base #=b#

The perimeter of a rectangle is made up of two of the base lengths and two of the height lengths.

#2b+2h=80#
#b+h=40#
#b=40-h#

From the second part of the question:

#h+5=4b#

Substituting the expression for #b#

#h+5=4*(40-h)#
#h=160-4h-5#
#5h=155#
#h=31#

Substituting this found value of #h# into the expression for #b#

#b=40-31#
#b=9#

#therefore# the dimensions of the rectangle are 31 feet by 9 feet