Question

A right triangle is dilated by a factor of 3.5. Which statements about the resulting triangle must be true? Select all that apply. (There is more than one answer)

It is smaller than the original triangle.

It is an isosceles triangle.

It is larger than the original triangle.

It is a right triangle

Answer 1

It is larger

it is a right triangle

Explanation:

When we talk of dilation, what we mean is that the original dimensions have increased or stretched them by the factor given.

So automatically, the new triangle will be bigger.

This means that the dilated triangle is larger than the original.

Since we do not know the original dimensions, we cannot say that is is an isosceles triangle.

The other second possible answer is that fact that it is a right triangle.

Let’s have a case of a Pythagorean triple 3,4 and 5

Let’s dilate by 3.5, so new dimensions become ; 10.5, 14 and 17.5 respectively

Now let’s square the other two sides and see if their sum would give the square of the biggest side which is the 3rd side

Thus, we have

10.5^2 + 14^2 = 17.5^2

The sum is exactly the same and thus we can conclude that the dilated triangle is also a right triangle