Question

Two similar triangles have a scale factor of 1:3. If the perimeter of the smaller triangle is 27, what is the perimeter of the larger?

Answer 1

Answer : 81 cm

Step-by-step explanation :

We know that, Scale factor tells us about the extent to which the larger ones is magnified from the smaller ones.

Scale factor = 1 : 3

This can be written as,

Ratio of Perimeters of two triangles = Scale factor.

Let the Perimeter of larger triangle = x

Now,

$\frac{1}{3} = \frac{27}{x} \\ \\ x = 27 \times 3 \\ \\ x = 81cm$

Therefore, Perimeter of the larger triangle is 81cm.

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How this works?

Let us think the sides of first triangle are x, y, z

And now, i will use a scale factor of 1 : 2

So, length of new sides will be 2x, 2y, 2z.

Now,
Perimeter of first triangle = x + y + z

Perimeter of second triangle = 2x + 2y + 2z = 2 ( x + y + z)

Ratio = x + y + z : 2x + 2y + 2z = 1 : 2 = Scale factor.

So, We can say that, Ratio of corresponding sides in other words, Scale factor will be equal to the ratio of Perimeters!