the area of a trapezoid varies jointly as the height, h, and the sum b1 and b2. find the constant of variation and the equation of joint variation if a=48 in^2 h=8 in b1 =5in b2 =7in

Question

Algabra 2 variations.

Answer 1

By saying the area varies jointly as the height, h, and the sum of b1 and b2, you are saying that the equation is

a = k (b1+b2) x h. To find the constant k, put in the values for a, b1, b2, and h, and solve for k. This turns out to be

k = 48 cm²/( (5 cm+ 7 cm) x 8 cm ) = 0.5 all the units cancel.

Placing the k value into the first expression given, you get

a= 0.5 x( b1 + b2) x h which is the formula for the area of a trapezoid ( 0.5 = 1/2).

Answer 2

a = kh(b₁ + b₂)

48 = k(8)(5 + 7)

48 = 96k

0.5 = k