The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 80 cm. What are the dimensions of the rectangle?

Question

The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 80 cm. What are the dimensions of the rectangle?

Answer 1

Hi Jamie! Good afternoon!! In order to set up an equation to solve the rectangle's dimensions, let the width br 'x' and the length in terms of x be 2x-5.

Thus 80 (Perimeter) = 2(x) + 2(2x-5)

Use the distributive property to multiply, so 2x + 4x-10 =80

Combine like terms (the x-terms) and 6x-10 = 80

Add 10 on both sides of the equation for 6x = 90

Divide each side by 6 and you get x=15 That's the width of the rectangle!

Plug 15 into the length given of 2(15)-5 and you get 25. There fore a rectangle with a width of 15 times 2 and a length of 25 times 2 equals 30 + 50 or 80. I hope that this helps!!!