College Algebra

Question

The area of a rectangular wall of a barn is 100 square feet. its length is 10 feet longer than twice its width find the length and width of the barn

Answer 1

Area_rectangle = L x W

Given: Area = 100 ft²

Length = 10 ft + 2W (10 ft more than twice the width)

Asked: L = ?, W = ?

Subsitute the expression for length into the Area equation: 100 ft² = (10 + 2W)(W) = 10W + 2W²

Rearrange the equation into quadratic form: 100 = 10W + 2W² becomes 2W² + 10W - 100 = 0

Solution to the quadratic equation: W = 5 ft, -10 ft; W cannot be a negative number

W = 5 ft

L = 2W + 10 = 20 ft