# Which set of ratios could be used to determine if one triangle is a dilation of the other?

###### Question:

## Answers

1 : 1.2

the little triangle gets 20% larger for the big triangle

[tex]\frac{4}{6}=\frac{6}{9}=\frac{8.5}{12.5}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

In this problem if the triangles are similar then , must be satisfy

[tex]\frac{4}{6}=\frac{6}{9}=\frac{8.5}{12.5}[/tex]

[tex]0.67=0.67=0.68[/tex] -----> is not true

therefore

The triangles are not similar

[tex]A.\ \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]

Step-by-step explanation:

Given

Let the two triangles be A and B

Sides of A: 4, 6 and 8.5

Sides of B: 6, 9 and 12.5

Required

Which set of ratio determines the dilation

To determine the dilation of a triangle over another;

We simply divide the side of a triangle by a similar side on the other triangle;

From the given parameters,

A ------------------B

4 is similar to 6

6 is similar to 9

8.5 is similar to 12.5

Ratio of dilation is as follows;

[tex]Dilation = \frac{4}{6}[/tex]

[tex]Dilation = \frac{6}{9}[/tex]

[tex]Dilation = \frac{8.5}{12.5}[/tex]

Combining the above ratios;

[tex]Dilation = \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]

From the list of given options, the correct option is A,

[tex]\frac{4}{6}[/tex] = [tex]\frac{6}{9}[/tex] = [tex]\frac{8.5}{12.5}[/tex]

Step-by-step explanation:

The set of ratios must have numerators coming from the same triangle and denominators coming from the same triangle. The other set of ratios have some numerators coming from both triangles and/or denominators coming from both triangles.

a

Step-by-step explanation:

Answer A

Step-by-step explanation:

Answer A is correct. Sides 3.6 and 3 form one ratio and sides 5.4 and 4.5 form another ratio of the lengths of corresponding sides.

Option (1).

Step-by-step explanation:

Dimensions of two triangles have been given as 3.6, 5.4, 6 units and 3, 4.5, 5 units.

If triangle one is dilated to form triangle two, then the ratio of the sides will be

Ratio = [tex]\frac{\text{Side of triangle (1)}}{\text{Corresponding side of triangle (2)}}[/tex]

= [tex]\frac{3.6}{3}[/tex]

Similarly, ratio of other two sides will be = [tex]\frac{5.4}{4.5}[/tex] and [tex]\frac{6}{5}[/tex]

Since the triangle (1) was dilated to form triangle (2), so both triangles will be similar and the ratios of their corresponding sides will be equal.

Therefore, Ratios of the sides = [tex]\frac{3.6}{3}=\frac{5.4}{4.5}=\frac{6}{5}[/tex]

Option (1) will be the answer.

See explanation

[tex]\frac{3.6}{3} = \frac{5.4}{4.5} = \frac{6}{5}[/tex]

Step-by-step explanation:

The two triangles are similar if the ratio of the corresponding sides are proportional.

The ratio of the corresponding sides are:

[tex]\frac{3.6}{3} = 1.2[/tex]

[tex]\frac{5.4}{4.5} = 1.2[/tex]

[tex]\frac{6}{5} = 1.2[/tex]

The set of ratios which could be used to determine if one triangle is a dilation of the other is

[tex]\frac{3.6}{3} = \frac{5.4}{4.5} = \frac{6}{5}[/tex]

If there are multiple correct options then check this one too.

[tex]\frac{3}{3.6} = \frac{4.5}{5.4} = \frac{5}{6}[/tex]

The ratio of the length of the triangles side can be used to determine if one triangle is a dilation of the other

Step-by-step explanation:

Dilation is the increase of the dimensions of a shape with respect to a scale factor. The scale factor determines how big the dilated shape is. The ratio of the length of the triangles side can be used to determine if one triangle is a dilation of the other

[tex]\frac{3.6}{3}=\frac{5.4}{4.5}=\frac{6}{5}=1.2[/tex]

So, the larger triangle is larger by 1.2 units.

The first answer is the correct one.

It is the only one that keeps all the ratios from the first triangle on the top and the 2nd triangle on the bottom. the other three answers keep swapping top and bottom positions.

47

step-by-step explanation:

2x^2+5x+17

your welcome. : )