Question

A parallelogram has a base of length 2x + 1 and a height of x + 3 and has an area of
42 square units. Find the base and height of the parallelogram. (A = BH)

Answer 1

Answer:

• base 7
• height 6

Step-by-step explanation:

Using the given expressions, we can write the area as ...

  A = BH

  42 = (2x +1)(x +3) = 2x^2 +7x +3

  2x ^2 +7x -39 = 0

  (x -3)(2x +13) = 0

  x = 3   or   -6.5  . . . . .  these values make the factors be zero

In order for the parallelogram to have positive dimensions, the value of x must be 3. So, the base and height are ...

  base = 2(3) +1 = 7

  height = 3 +3 = 6

Answer 2

Answer: height = 6 units

Base = 7 units

Step-by-step explanation:

The formula for determining the area of a parallelogram is expressed as

Area = BH

B = 2x + 1

H = x + 3

If area = 42 square units, then

(2x + 1)(x + 3) = 42

2x² + 6x + x + 3 = 42

2x² + 7x + 3 - 42 = 0

2x² + 7x - 39 = 0

2x² + 13x - 6x - 39 = 0

x(2x + 13) - 3(2x + 13) = 0

x - 3 = 0 or 2x + 13 = 0

x = 3 or x = - 13/2 = - 6.5

Since x cannot be negative, then x = 3

Therefore,

Base = 2x + 1 = 2 × 3 + 1 = 7 units

Height = x + 3 = 3 + 3 = 6 units