The length of a rectangular piece of land is 50 ft more than two times it’s width. The perimeter is 640 ft. Find it’s dimensions.

Answer 1

Hi Tay

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

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: 2w + 50

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

640 = 2 • (2w + 50) + 2 • w

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

640 = 4w + 100 + 2w

640 = 6w + 100

640 - 100 = 6w + 100 - 100

540 = 6w

540/6 = 6w/6

90 = w

The width of the rectangle is 90 feet.

The length will be 2 •90 + 50 = 180 + 50 = 230 feet

To verify:

Perimeter = 2 • 90 + 2 • 230 = 180 + 460 = 640 feet

Hope this helps Tay. Let me know if you have further questions or would like to schedule a lesson (online is available if you prefer). Take care.