Question

What side lengths would make Triangle ABC and Triangle DEF similar?

Hint: What is scale factor that takes AB to DE?

Answer 1

A. DF = 2 units and EF = 1.4 units

Explanation:

Two triangles are said to be similar if they have the same angles, but not necessarily the same size.

In similar triangles, the corresponding sides are proportional. This means that the ratio of the lengths of two corresponding sides in one triangle is the same as the ratio of the lengths of the corresponding sides in the other triangle.

So,

In this case:

`\sf (AB)/(DE) =(BC)/(EF)=(AC)/(DF)`

Substitute known value:

`\sf (2)/(1) =(3)/(EF)=(4)/(DF)`

So, Scale factor AB to DE is 2:1.

We can find the unknown side by comparing two of them.

So,

`\sf (2)/(1) =(3)/(EF)`

Doing Criss cross Multiplication:

2EF = 3 × 1

Divide both sides by 2.

`\sf EF =( 3)/(2)\\\\ = 1.5`

So,

EF = 1.5 units

Similarly

`\sf (2)/(1) =(4)/(DF)`

Doing Criss cross Multiplication:

2DF= 4 × 1

Divide both sides by 2.

`\sf DF =(4)/(2)\\\\ = 2`

So,

DF = 2 units

Therefore,the answer is:

A. DF = 2 units and EF = 1.4 units