The perimeter of a rectangle is 54cm, the area of the same rectangle is 176cm squared, what is the dimensions of the rectangle?

1 Answer
Mar 27, 2018

Answer:

11 by 16

Explanation:

Set up two equations

# 2x + 2y = 54 #

# x xx y = 176#

Solving the first equation for x

# 2x + 2y -2y = 54 - 2y# this gives

# 2x = 54 - 2y# Divide both sides by 2

# (2x/2) = ( 54 -2y)/2 # This gives.

# x = 27 - y # putting this value into the second equation gives.

# ( 27-y)xx y = 176 # multiplying across the parenthesis gives

# 27y - y^2 = 176# subtracting 176 from both sides gives
is
# 27y - y^2 - 176 =0 # multiplying by negative one gives

# -27y + y^2 + 176 = 0 # factoring this into y gives

# ( y -11) xx (y -16) = 0 # Solving for both y's gives

# y = 11 , y = 16 #