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

Question

8471 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-27T01:23:53

11 by 16

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 #