Question

Jakob and his friends have collected 160 ft² of fabric with which to sew a backdrop for a play. Jakob wants to use all the material, and he would like the backdrop to be a golden rectangle. If Jakob uses the approximate ratio of 8 to 5, then he can use the equation 85w2=160 to determine the width, w, of the backdrop. What is the width of the backdrop?

Answer 1

To solve the equation 85w^2=160 for w, we need to isolate w on one side of the equation.

First, divide both sides by 85:

85w^2/85 = 160/85

Simplifying, we get:

w^2 = 1.88235294118

To solve for w, we need to take the square root of both sides:

sqrt(w^2) = sqrt(1.88235294118)

Since w is a positive length, we can drop the negative square root, so we have:

w = 1.3725...

Rounding to the nearest hundredth, we get:

w ≈ 1.37 ft

Therefore, the width of the backdrop is approximately 1.37 feet.