Area of a rectangle help?

Question

One side of a rectangle is 5 in longer than five times another side. The area of the rectangle is 210 in^2. Find the length of the longer side.

Answer 1

The longest side is 35 inches

We can set up a quadratic to find the side

For a rectangle the area is Length x Width, L X W

Let Length be the longer side

Let Width be the shorter side

Where

L = 5W + 5

Area = W(5W + 5)

210 = 5W² + 5W

0 = 5W² + 5W - 210

Divide both sides of the equation by 5

0 = W² + W - 42

This can be factored into

(W + 7)(W - 6)

since W cannot be negative, W can only be 6

The longer side is 5W + 5

5(6) + 5 = 35

Or

0 = 5W² + 5W - 210

(5W + 35)(W - 6)

Again since W cannot be negative, W can only be 6

Checking

210 = W(5W + 5)

210 =6(5*6 + 5)

210 = 6(30 + 5)

210 = 6(35)

210 = 210.

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