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a right square pyramid has a base with sides that are 2 inches in length and a slant height of 7 inches. if the lengths of the sides of the base and the slant height are multiplied by 7, by what factor is the surface area multiplied?

a.7
b.14
c.28
d.49

The answer is D: 49

Step-by-step explanation:

If you multiply the scale factor, or 7, by itself, you get 7*7= 49

(don't worry, I just took the test, this is the correct answer)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240