The base of a parallelogram is 4 inches longer than twice the height. The area of the parallelogram is 16 square inches. What is the height?

2 inches

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the height )

Here A = 16 and b = 2h + 4 ( 4 more than twice the height ), thus

16 = h(2h + 4) = 2h²  + 4h ( subtract 16 from both sides )

2h² + 4h - 16 = 0 ( divide through by 2 )

h² + 2h - 8 = 0 ← in standard form

(h + 4)(h - 2) = 0 ← in factored form

Equate each factor to zero and solve for h

h + 4 = 0 ⇒ h = - 4

h - 2 = 0 ⇒ h = 2

But h > 0 thus h = 2

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x