Question

Alani is in charge of marketing for a travel company. She is designing a brochure that will have 6 photos. Suppose the dimensions of the narrower photos were increased to 2 in. by x in. What expression would represent the new arrangement based on the GCF?

Answer 1

Complete Question

Alani is in charge of marketing for a travel company. She is designing a brochure that will have 6 photos.

There are two main photos each of length x cm.

There are 4 long pictures each of 1 inch by x cm.

(a)Find the total area of the photos

(b)Find a rectangular arrangement of the photos and determine the factoring that represents this arrangement.

(c)Suppose the dimensions of the narrower photos were increased to 2 in. by x in. What expression would represent the new arrangement based on the GCF?

Answer:

(a)
`2x^2+4x`

(b)2x(x+2)

(c)
`2x(x+4) sq. units`

Explanation:

(a)Area of the Photos

Total Area =2(Area of Main Photos)+4(Area of Long Pictures)

`=2(x^2)+4(1*x)\\=2x^2+4x`

(b)If we arrange the six photos in a rectangular array

We would have a photo of:

Height = x

Width =x+x+4 =2x+4

Therefore:

Area =x(2x+4)

We can factorize further to obtain:

Area =2x(x+2) sq. in.

(c)If the dimensions of the narrower photos were increased to 2 in. by x in.

Total Area =2(Area of Main Photos)+4(Area of Long Pictures)

`=2(x^2)+4(2*x)\\=2x^2+8x\\$Factoring out the GCF, we obtain\\Area=2x(x+4) sq. units`

The expression that would represent the new arrangement based on the GCF is: 2x(x+4)