Question

The perimeter of triangle B is 2.5 times greater than the perimeter of triangle A.The area of triangle B is how many times greater than the area of triangle A?


A. 1.25 times greater

B. 2.5 times greater

C. 6.25 times greater

D. 25 times greater

Answer 1

i googled this

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.

The scale factor in area is squared. Since the scale factor of the areas are 1:25, you take the square root of both, and your result is the new scale factor.

area goes up in proportion to a linear dimension squared.
So if the perimeter goes up by 5x, the area goes up by 5²x or 25x