Question

If the height of a parallelogram is 4 times more than it’s base, and the area is 221 sq in, what is the base and height?

Answer 1

Base = 13 inches

Height = 17 inches

Explanation:

The formula to find the area of a parallelogram = Base × Height

Let's represent Base = B

Height = H

From the question, the height is 4 times more than the Base

Height(H) = B + 4

Area = 221 square inches

Therefore, area of a parallelogram = Base × Height

221 sq in = B ×( B+4)

221 sq in = B² + 4B

B² + 4B - 221 = 0

We would solve the quadratic equation using factorisation method. Hence,

B² + 17B - 13B - 221 = 0

(B²+ 17B) - (13B - 221) = 0

B(B + 17) - 13(B + 17) = 0

(B + 17) (B - 13) = 0

B + 17 = 0

B = - 17

Or

B - 13 = 0

B = 13.

From the above calculation, since B = Base

B = -17 inches Or 13 inches

The base of a parallelogram cannot be negative, hence , The Base of the Parallelogram = 13 inches.

We are told that the height of the Parallelogram is 4 times more than the Base. This was represented but the equation

B + 4 = H

Since B = 13 :

13 + 4 = H

Height(H) = 17 inches.

Therefore, The base of the Parallelogram is 13 inches while the height of the Parallelogram is 17 inches.

Answer 2

Base = 13in

Height = 17in

Explanation:

Explanation:

height of a parallelogram = 4 times more than it’s base

Let height = H

Base = B

H = 4 + B

area of the parallelogram = 221 in²

area of the parallelogram = base × height

221 = B × H = B × (4+B)

221 = 4B + B²

B² + 4B - 221 = 0

Using almighty formula to find B

See attachment for explanation

From the calculation:

Since the dimension of the parallelogram can't be negative, B = 13in

Height = B + 4 = 13+4

Height = 17in