Question

The area of a rectangle varies jointly as its length and width. Find the equation of joint variation if A = 60ft², l = 15ft, and w = 4ft.
A. A = lw
B. A = 2lw
C. A = 3lw
D. A = 4lw

Please give explanation/steps, thank you! :)
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Answer 1

Answer:

A

Step-by-step explanation:

Given A varies directly as l and w then the equation relating them is

A = klw ← k is the constant of variation

To find k use the condition A = 60, l = 15 and w = 4 , then

60 = k × 15 × 4 = 60k ( divide both sides by 60 )

1 = k

A = lw ← equation of variation

Answer 2

Answer: The length is 6 feet and the width is 10 feet.

Step-by-step explanation: The question has specified the area as 60 (square feet) and the length and width are yet unknown. However we know that the length is 4 feet less than the width. What this means is that, if the width is W, then the length is W - 4.

We can now write an equation for the area of the rectangle as follows;

Area = L x W

60 = (W - 4) x W

60 = W^2 - 4W

If we rearrange all terms on one side of the equation, we now have

W^2 - 4W - 60 = 0

This is a quadratic equation and by factorizing, we now have

(W + 6) (W - 10) = 0

Hence,

Either W + 6 = 0 and then W = -6

Or W - 10 = 0 and then W = 10

We know that the side of the rectangle cannot be a negative value, so we go with W = 10.

Having calculated W as 10, the length now becomes

L = W - 4

L = 10 - 4

L = 6

Therefore, length = 6 feet and width = 10 feet