the length of a rectangle is sixteen more than twice it’s width. if the perimeter is 92 inches what are the dimensions of the rectangle?

Answer 1

The variable w represents the width of the rectangle and the variable l represents the length of the rectangle.

Since the length is 16 more than twice the width, we can write:

l = 16 + 2w

Also perimeter is equal to 2 times the length plus 2 times the width, so we can write:

P = 2l + 2w

We can substitute 16 + 2w for L and write:

P = 2 (16 + 2w) + 2w

Since the perimeter is 92 inches, we can write:

92 = 2 (16 + 2w) + 2w

Now use the distributive property and combining like terms to solve for w:

92 = 2 (16 + 2w) + 2w

92 = 32+ 4 w + 2w

92 = 32 +6w

92-32 = 32 + 6w -32

60 = 6w

60/6 = 6w/6

10 inches = w

The length will be 16 + 2w OR 16 + 2* 10 = 36 inches

To check: 10 inches + 10 inches + 36 inches + 36 inches = 92 inches