Question 674518
With this question, break down the sentence into bits and pieces.

"The width of a rectangle is..."

w =


"1 foot shorter than half the length."

{{{ 1/2 }}} l - 1


"If the perimeter of the rectangle is 64 feet..." 

P = 64
 (NOTE: Remember P = 2l + 2w)


"Find the dimensions of the rectangle."

Find "l" and "w."


Now that we have those, we piece it all together.

w = {{{ 1/2 }}} l - 1

P = 2l + 2w

64 = 2l + 2({{{ 1/2 }}} l - 1)


Use the distributive property.

64 = 2l + l - 2


Combine like terms, and add two to both sides.

66 = 3l


Divide both sides by 3.

22 = l


Now that we have "l," we can find "w" by plugging it into w = {{{ 1/2 }}} l - 1.

{{{ 1/2 }}} * 22 - 1


Solve.

11 - 1 = 10



length = 22

width = 10



Check your work.


P = 2l + 2w
64 = (2 * 22) + (2 * 10)
64 = 44 + 20
64 = 64