Question

The area of a rectangular wall of a barn is 64 square feet. It’s length is 12 feet longer than the width. Find the length and width of the wall of the barn

Answer 1

Length of wall is 16 feet and breadth is 4 feet.

Explanation:

• Step 1: Given area = 64 sq. ft, length is breadth + 12 ft. Let breadth be b.

So length, l = b + 12

• Step 2: Substitute in area for rectangle = length * breadth

⇒ (b + 12) * b = 64

⇒ b² + 12b = 64

⇒ b² + 12b - 64 = 0

• Step 3: Solve for b using equation for finding roots of quadratic equation

Roots = (- b ±√b² - 4ac)/2a

⇒ b = (- 12 ±√144 - 4 * 1 * - 64)/2

= (-12 ±√144+256)/2 = (-12±√400)/2

= (-12±20)/2

= 4, -16 (negative is neglected)

⇒ breadth is 4 feet

• Step 4: Length = b + 12 = 16 feet