203k views
4 votes
Beth enlarged the triangle below by a scale of 5. The original triangle had a base of 3.5 cm and a height of 4 cm. She found the area of the enlarged triangle using the formula (base)(height)(scale). However, she made an error in her calculation. What was Beth's error?

User Kvothe
by
8.3k points

1 Answer

5 votes

She should have used this formula

0.5(base)(height)(scale)^2

where the 0.5(base)(height) portion is the area of the original triangle. Beth forgot about the 0.5 out front, aka 1/2. She also forgot to square the "scale" part.

Why do we square the "scale" part? Consider a triangle with base b and height h. Its area is 0.5bh

Now let's scale using the linear factor k. The base b turns into bk. The height turns into hk.

Then,

new area = 0.5*(new base)*(new height)

new area = 0.5*(bk)*(hk)

new area = 0.5bh*k^2

We have the k^2 at the end to signal we square the linear scale factor to get the area scale factor. This applies to any dilated shape. It doesn't have to be a triangle.

If 0 < k < 1, then the shape shrinks. If k > 1, then the shape enlarges.

User SachinSunny
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories