a rectangle has a perimeter of 324 inches. the width is 6 inches less than half the length. what are the length and width of the rectangle?

Question

a rectangle has a perimeter of 324 inches. the width is 6 inches less than half the length. what are the length and width of the rectangle?

Answer 1

Hello Vero!

The perimeter of a rectangle is P = 2L + 2W where L is the length and W is the width

We are given the perimeter and a relationship between length and width.

[1] 324 = 2L + 2W

We have to convert the relationship between the length and the width into words, which is the trickiest part of this problem. The relationship mathematically is:

[2] W = .5L - 6

We have two equations and two unknowns, so we can plug W from [2] into [1] and solve for L.

324 = 2L + 2(.5L - 6)

Solving for L we get:

[3] L = 112 inches

For the final step, we can plug L from [3] into [1] to get W

324 = 2(112) + 2W

Solving for W we get:

[4] W = 50 inches

Since we should always check our answers, we can plug in the Length and Width into the first equation.

324 = 2(112) + 2(50) = 324

Let me know if you need further clarification :)