Question

Luisa knit a rectangular scarf that measures 4 feet by 1 foot. She wants to use the remaining 6 square feet of fabric to create a border around the scarf.
Which equation can she use to find the required width of the border x?

Answer 1

To solve this problem, let us recall that the formula for Area of a rectangle is:

A = l * w

Where,

l = length of one side = 4 ft

w = width of one side = 1 ft

Therefore the original area is:

Ao = 4 ft * 1 ft

Ao = 4 ft^2

 

Since each border would be increased by x, therefore the new l and w would be:

l = 4 + 2x

w = 1 + 2x

The new area becomes:

A = (4 + 2x) (1 + 2x)

 

The difference of the two would be the area of the remaining scarf:

A – Ao = 6 square ft

(4 + 2x) (1 + 2x) – 4 = 6             ---> 1

(4 + 2x) (1 + 2x) = 10                 ---> 2

The equation to use can be equation 1 or equation 2.