Question

Use the diagram below to find the lengths of the missing sides. Figures in each diagram are similar.

X=15
X=10
X=40
X=30

Answer 1

DE/AB=DF/AC

10/5=DF/15

=10×15=5DF

=150=5DF

DF=150÷5

=30

Answer 2

Such triangles do not exist.

Explanation:

There is some mistake in your question.

We know:

In any triangle with sides a, b and c:

a + b > c

a + c > b

b + c > a

In your question the triangle ABC has:

a = 5, b = 10, c = 15

then

5 + 10 = 15 not > 15.

a + b = c not > c.

In my opinion, the question makes no mathematical sense.

Nevertheless, the moderator asked me to correct my answer.

If two triangles are similar, then corresponding sides are in proportion.

`(10)/(5)=(20)/(10)=(x)/(15)\\\\2=2=(x)/(15)\\\\(x)/(15)=2\Rightarrow x=30`