Finding the length of a square given the perimeter and 2 sides

Question

The perimeter of the rectangle below is 112 units. Find the length of side BC. Side AD is 5x-1 and Side DC is 4x+3. Write your answer without variables. 

Answer 1

For any rectangle, the perimeter is found by adding up all the sides.  A rectangle has 2 pairs of sides that are equal.

 

This comes out to P = 2(length) + 2(width)

 

We can call the length the value of AD and the width the value of DC.

 

So, we have P = 2(5x - 1) + 2(4x+3) = 10x - 2 + 8x + 6 = 18x + 4

 

18x + 4 = 112

       - 4      - 4

 

18x = 108

 

Dividing by 18 to both sides gives the value of x as 6.

 

Now, we find the specific value of BC, we only need the value of side AD.  (You can draw a figure if it helps you see why we only need side AD)

 

AD = 5(6) - 1 = 30 - 1 = 29

 

So length BC = 29 units