A rectangular yard has a length that is 16 yards longer than its width(w). If the perimeter of the yard is 96 yards, find the dimensions of the yard

Answer 1

This problem can be solved by creating an equation and solving it to find the dimensions of the yard.

As stated in the problem, let's use the variable w to represent the width of the rectangle.

Then we can write the following expression to represent the length of the rectangle: w + 16

Since the perimeter of a rectangle can be calculated by adding 2 times the length to 2 times the width , we can write the following equation for the perimeter (P) of the rectangle:

P = 2 • length + 2 • width

96 = 2 • (w + 16) + 2 • w

Now use the distributive property, combining like terms, and inverse operations to determine the value of w:

96 = 2w + 32 + 2w

96 = 4w + 32

96 - 32 = 4w + 32 - 32

64 = 4w

64/4 = 4w/4

16 = w

The width of the rectangle is 16 yards.

The length will be 16 + 16 = 32 yards

To verify:

Perimeter = 2 • 32 + 2 • 16 = 64 + 32 = 96 yards