The width of a rectangle is 5 more than one-fourth of its length, and the perimeter is 40 cm. What is the length and width?

Question

I tried solving this, but I have absolutely no clue how to.

Answer 1

Hi Taylor.

 

Let's try to set this up.

 

Let w = width of rectangle

L = length of rectangle

P = perimeter = 2L + 2W = 2(L+W)

We also are told that W = 5+(1/4)L and P = 40

 

If P = 2(L+W), let's substitute what we know.

 

40 = 2 (L+W)

40 = 2 [L + 5+(1/4)L]

40 = 2 [(5/4)L +5]

 

Solving for L

20 = (5/4)L +5

15 = (5/4)L

12 = L

 

Since W = (1/4)L + 5,

W = (1/4)12 + 5

W = 3+5 = 8

 

Now checking to see if we are right

2L + 2W = 40

2(12) + 2(8) = 24 + 16 = 40