Two regular polygons with the same number of sides have sides of 6 inches and 8 inches respectively. Find the ratio of their perimeters.
Please be detailed!!

The ratios of their perimeters is 3/4

Step-by-step explanation:

In this question, we are asked to find the ratio of two perimeter of different regular polygons having the same number of sides but different side lengths.

A regular polygon is a polygon that has its all its sides to be of equal lengths. Now to find the perimeter of this kind of polygon, what we need to do is to multiply the number of sides that we have by the length of one of the sides.

Now, since we know that the number of sides of the polygons are equal, we can say that both polygons each have a total length of n sides each.

For the 6 inch side polygon, the perimeter of the polygon would be 6 * n = 6n inches

For the 8 inch side polygon, the perimeter of the polygon would be 8 * n = 8n inches

The ratio of the two thus becomes;

6n : 8n

This is same as writing 6n/8n

This is equal to 3:4 to the lowest ratio( we first divide by n on both sides, then 2 after wards to arrive at this answer.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

the answer is a.

135 and 80

step-by-step explanation: