Question

The rectangle has an area of 60 square feet. Find its dimensions (in ft). (x + 4) feet smaller value ___________________ ft larger value ____________________ ft

Answer 1

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The rectangle has an area of 60 square feet. Find its dimensions (in ft) if the length of the rectangle is 4 ft more than its widh.

smaller value ___________________ ft

larger value ____________________ ft

Answer:

Smaller value = 6 ft

Larger value = 10 ft

Step-by-step explanation:

Recall that the area of a rectangle is given by

`Area = W * L`

Where W is the width and L is the length of the rectangle.

It is given that the rectangle has an area of 60 square feet.

`Area = 60 \: ft^2 \\\\60 = W * L \\\\`

It is also given that the length of the rectangle is 4 ft more than its width

`L = W + 4`

Substitute
`L = W + 4` into the above equation

`60 = W * (W + 4) \\\\60 = W^2 + 4W \\\\W^2 + 4W - 60 = 0 \\\\`

So we are left with a quadratic equation.

We may solve the quadratic equation using the factorization method

`W^2 + 10W - 6W - 60 \\\\W(W + 10) – 6(W + 10) \\\\(W + 10) (W - 6) = 0 \\\\`

So,

`(W + 10) = 0 \\\\W = -10 \\\\`

Since width cannot be negative, discard the negative value of W

`(W - 6) = 0 \\\\W = 6 \: ft \\\\`

The length of the rectangle is

`L = W + 4 \\\\L = 6 + 4 \\\\L = 10 \: ft \\\\`

Therefore, the dimensions of the rectangle are

Smaller value = 6 ft

Larger value = 10 ft

Verification:

`Area = W * L \\\\Area = 6 * 10 \\\\Area = 60 \: ft^2 \\\\`

Hence verified.