A rectangular building has a perimeter of 208 meters. It's area is 2415 square meters. What are the dimensions of the building?

Step-by-step explanation:

Perimeter of rectangle = 208 m

2 * (l + w) = 208 {divide both sides by 2}

l + w = 208/2

l + w = 104

l = 104 - w

Area of rectangle = 2415 square meters

l*w = 2415

Substitute l = 104 - w in the above equation,

(104 - w) * w = 2415

104w - w² = 2415

0 = 2415 - 104w + w²

w² - 104w + 2415 = 0

Sum = - 104

Product = 2415

Factors = (-69), (-35)

w² - 35w - 69w + (-69) * (-35) = 0

w (w - 35) - 69 (w - 35) = 0

(w - 35) (w - 69)

w - 35 = 0; w - 69 = 0

w = 35; w = 69

The dimensions of the building: 35, 69