Arectangle has an area of 105 square feet. if the sum of the length and the width is 26 feet, find the dimensions. include units in your answer.

L x W = 105

L + W = 26 so L = 26 - W

substitute L = 26 - W into L x W = 105

(26 - W) x W = 105

26W - W^2 = 105

W^2 - 26W + 105 = 0

(W - 21)(W - 5) = 0

W - 21 = 0; W = 21

W - 5 = 0; W = 5

The the dimensions of the rectangle are 5 ft and 21 ft.

Double check:

The sum of the length and the width is 26 feet: 21 + 5 = 26 feet

A rectangle has an area of 105 square feet: 21 x 5 = 105 square feet

false

step-by-step explanation:

false.   two legs of the trapezoid would be congruent, but the other two would not.   were all the legs congruent, then we'd have a square; were the 2 shorter sides congruent and the 2 longer sides also congruent, we'd have a rectangle.