Question

∆ABC is similar to ∆DEF. The perimeter of ∆ABC is five times the perimeter of ∆DEF.
The area of ∆ABC is 100 square centimeters. The area of ∆DEF is ____ square centimeters.

2
4
10
20

Answer 1

20?

Answer 2

100 divided by 5 =20

Answer 3

Nope.

Answer 4

it was a wild guess

Answer 5

Scale factor is 5.

Answer 6

Divide area by half first

Answer 7

100 /2 = 50

Answer 8

Look at the squares in the figure above.
The left square has side 2 cm and perimeter 8 cm. Its area is 4 cm^2.
The right square has side 4 cm and perimeter 16 cm. Its area is 16 cm^2.

Notice that the length of the side of the right square is twice the side of the left square.
The perimeter is also twice.
The scale factor is 2.

Notice what happened to the ares of the squares.
(16 cm^2) / (4 cm^2) = 4

The ratio of the areas is not 2, but 4.
4 happens to be 2^2.

When you apply a scale factor of k to the linear dimensions of a figure (lengths of sides, radius of circle, perimeter, etc.) the area changes by a factor of k^2.

Answer 9

In your case, the perimeters have a scale factor of 5.
Perimeters are linear dimensions.
If the perimeters have a scale factor of 5, what is the ratio of the areas?

Answer 10

10

Answer 11

No.
10 = 5 * 2
You need to raise the scale factor to the 2nd power.
What is 5^2 = ?

Answer 12

25

Answer 13

Correct.
If a triangle has linear dimensions 5 times the size of another triangle, then its area is 25 times as large.

Answer 14

Can you find the areas of the two triangles below?
Notice that the larger triangle has sides that are 5 times the length of the sides of the smaller triangle.