Question

Assuming that the triangles below are similar? How do I find the scale factor and the length of the missing sides?

Scale Factor: _
a= _
b= _

Answer 1

Hint: From the question given we have to find the scale factor and the length of the missing sides. As they said that given triangles are similar so the ratio of corresponding sides are equal. Scale factor means it is the ratio of any two corresponding lengths in two similar geometrical figures. By the definition we can find the scale factor of above a and b.

Complete step by step solution:
We know that in similar triangles
The ratio of corresponding sides is equal.
We know that scale factor,
Scale factor means it is the ratio of any two corresponding lengths in two similar geometrical figures
First, we will solve the figure a
In (a)
The corresponding sides are $$5$$ and $$15$$
Therefore, the scale factor is
$$\Rightarrow scalefactor={\displaystyle \frac{15}{5}}=3$$
$$3$$means the right-side triangle is an enlargement of the left side triangle.
By observing the figure, the triangle on the right is an enlargement of the triangle on the left side of the triangle.
By this we can find the value of the length of the side of the left triangle by multiplying the corresponding side length of the right triangle to the scale factor we will get the length of the side.
So, the length of the left side triangle let the length is a then the values of a is
$$\Rightarrow a=3\times 3=9$$
now we will move to the figure b
in (b)
The corresponding sides are $$3$$ and $$5$$
Therefore, the scale factor is
$$\Rightarrow scalefactor={\displaystyle \frac{12}{20}}={\displaystyle \frac{3}{5}}$$
$${\displaystyle \frac{3}{5}}$$ means the right-side triangle is a reduction of the left side triangle.
By observing the figure, the triangle on the right is a reduction of the triangle on the left side of the triangle.
By this we can find the value of the length of the side of the left triangle by multiplying the corresponding side length of the right triangle to the scale factor we will get the length of the side.
So, the length of the left side triangle let the length is b then the values of b is
$$\Rightarrow b=15\times {\displaystyle \frac{3}{5}}=9$$

Note:
Students should know the concept of scale factor and know the meaning of the term similar by seeing that term students should strike the term similar means the ratio of the corresponding sides are equal.