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

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

Step-by-step 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