Find the greatest common factor of 8a3b2 and 12ab4

You can find the GCF of these two terms by finding the GCF of the individual parts. I'll start off with 8 and 12. You can find their GCF by making a list of their factors.

8: 1, 2, 4, 8
12: 1, 2, 3, 4, 6, 12

So, the first part of your GCF will be 4.

Next, find the GCF of the variables. Do this by listing the variables in each term.

Term 1: a , a , a , b , b
Term 2: a , b , b , b , b

They each have at least one a and two b's, so those will be the second parts of your GCF. Now, put them all together with the number first and then the variable with the higher power.

4b^2a

165 ft

Step-by-step Explanation:

==>Given:

Quadrilateral ABCD (scaled-down model of walkway) ~ Quadrilateral EFGH (walkway)

EF = 60ft

AB = 4 in

BC = 2 in

CD = 2 in

DA = 3 in

==>Required:

Total length (Perimeter) of actual walkway.

==>Solution:

Since ABCD ~ EFGH, the ratio of their corresponding sides would be the same.

Thus, it means, EF/AB = FG/BC = GH/CD = HE/DA

Since, we know the length of one side of Quadrilateral EFGH, we can find the scale factor, which we would use in solving for the perimeter of Quadrilateral EFGH.

EF = 60 ft

AB = 4 in

EF/AB = scale factor

Note: 60 ft should be converted to inches. Both corresponding side must be in the same unit if we are to set their ratio.

1 ft = 12 in

Therefore, 60 ft = 60 × 12 = 720 in = EF

720/4 = 180

The scale factor = 180.

Calculate the total length of Quadrilateral ABCD

Perimeter/total length = AB + BC + CD + DA

= 4 + 2 + 2 + 3

= 11 inches

Find the total length of Quadrilateral EFGH by multiplying the perimeter of ABCD (11 inches) by the scale factor we got (180)

Perimeter of EFGH = 11 × 180 = 1,980 inches

Convert the total length to ft

12 in = 1 ft

1,980 in = 1,980/12 = 165 ft

Total length of of the actual walkway (EFGH) = 165 ft