Question

A frame around a rectangular family portrait has a perimeter of 150 inches. The length is ten more than four times the width. Find the length and width of the frame.

Answer 1

Length = 62 inches, Width = 13 inches

Explanation:

Let L represent the length of the frame, W, the width and P, the perimeter

Perimeter of a rectangle, P = 2 (L + W) .....eq 1

Also, P = 150 inches

and

L = 10 + 4W .....eq 2

Slotting in the respective values of P and L in eq 1

150 = 2 {(10 + 4W) + W}

Expanding the bracket

150 + 2 (10 + 5W)

150 = 20 + 10W

Subtracting 20 from both sides of the equation

150 - 20 = 20 - 20 + 10W

130 = 10W

Dividing both sides by the coefficient of W which is 10

13 = W

Therefore, W = 13 inches

Slotting in the value of W in eq 2

L = 10 + 4 (13)

L = 10 + 52

L = 62 inches

Lets ensure that the values of L and W are correct

P = 2 (L + W)

150 = 2 (13 + 62)

150 = 2(75)

150 = 150

Hence, L = 62 inches, W = 13 inches

Answer 2

Answer: The length is 62 inches and the width is 13 inches

Step-by-step explanation: The perimeter of the rectangular portrait has been given as 150 inches. We also know that the perimeter of a rectangle is given as

Perimeter= 2(L + W)

However we don't have the measurements for the length and width. What we do have are descriptions of both. The length is given as W, while the length is ten more than four times the width. That is, the length equals

10 + 4W

Therefore we have the length and the width as

L = 4W + 10 and

W = W

If the perimeter is 150, and

Perimeter = 2(L + W) then,

150 = 2(4W + 10 + W)

150 = 2(5W + 10)

150 = 10W + 20

Subtract 20 from both sides of the equation

130 = 10W

Divide both sides of the equation by 10

13 = W

With that in mind we can now calculate the length as

L = 4W + 10

Substitute for the value of W

L = 4(13) + 10

L = 52 + 10

L = 62

Therefore, the length is 62 inches and the width is 13 inches