Question

Please Help! 10 points!

A) The perimeter of triangle 2 is 1.5 times the perimeter of triangle 1. The area of triangle 2 is how many times bigger than the area of triangle 1?

B) The area of triangle 4 is four times the area of triangle 3. The perimeter of triangle 4 is how many times bigger than the perimeter of triangle 3?

Answer 1

D.

Explanation:

Are the two triangles supposed to be similar? Because otherwise I don't see how you can do this. It's possible to have two different triangles of the same area but different perimeters, which means given a triangle, you could make two different triangles that have different perimeters yet both have an area 25 times greater than the original.

If they're similar, then let b and h be the height of triangle A. then the base and height of triangle B are bx and hx for some unknown value of x, which means its area is (1/2)(bx)(hx) = (1/2)bh * x^2. To get this to be 25 times the area of A, (1/2)bh, just let x=5. This means the perimeter should be 5 times greater.

Answer 2

Part A)

Answer: 2.25

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You find this by squaring 1.5 to get (1.5)^2 = (1.5)*(1.5) = 2.25

Consider a rectangle that is 10 by 4, so its area is 40. Multiply each dimension by 1.5 and we get a 15 by 6 rectangle, so the new area is 90. Note how dividing 90 over 40 leads to 2.25, which is the proper area scale factor.

This example of using a rectangle can be extended to any other geometric shape.

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Part B)

Answer: 2

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Go in reverse of what happened in part A. Instead of squaring, we apply the square root. The square root of 4 is 2, so this is the scale factor between the perimeters.

Consider a rectangle that is 5 by 10, so it has area 50. Then consider another rectangle that is 10 by 20, with area 200. The jump from 50 to 200 has us multiply by 4, meaning the larger rectangle's area is four times larger.

Going from 5 to 10 is a jump of "times 2", so is the jump from 10 to 20. So each dimension has been multiplied by 2. Consequently, the old perimeter has been doubled to get the new one.