Question

You are designing a gift card that has a border along one side, as shown. The area of the white part of the card is 30 Square centimeters. What is the area of the border?

Answer 1

The area of the white rectangle is length * width and is 30 cm^2.

LW = A

Replace L with r and W with r + 1.

r(r + 1) = 30

Distribute the r.

r^2 + r = 30

Subtract 30 from both sides.

r^2 + r - 30 = 0

Factor the polynomial.
We need two numbers that multiply to -30 and add to 1.
They are 6 and -5.

(r + 6)(r - 5) = 0

r + 6 = 0   or   r - 5 = 0

r = -6   or   r = 5

A dimension of a rectangle (length or width) cannot be a negative number, so we discard the negative answer, r = -6. We keep the answer r = 5.

Now that we know r = 5, the border is r by 2 cm, but r = 5 cm, so the border is 5 cm by 2 cm.

A = LW = 5 cm * 2 cm = 10 cm^2

Answer: The area of the border is 10 cm^2.

Answer 2

R=5

r(r-1)=30
r²+r=30
5²+5=30
5²=30-5
5²=25
5=5

Black box = r x 2
5 x 2 = 10

Black part of card is 10 sq cm.