In the figure below, the segment is parallel to one side of the triangle. The ratio of 12 to y is 1:2 1:3 1:4 2:3

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eudora eudora · Answer 1 · 2019-05-08T00:03:50+02:00

Answer:

Option B. 1 : 3

Step-by-step explanation:

There are two triangles shown in the picture attached ΔABC and ΔCD.

In these triangles sides AB and DE are parallel and BC is transverse line so ∠ABC = ∠EDC (corresponding angles)

Similarly AC is transverse to parallel lines AB and DE, so ∠BAC = ∠DEC (corresponding angles)

∠ACB is common in both the triangles.

Therefore ΔABC and ΔDEC are similar.

We know in similar triangles corresponding sides are in the same ratio.

[tex]\frac{AB}{ED}=\frac{AC}{EC}[/tex]

[tex]\frac{y}{12}=\frac{30+15}{15}=\frac{45}{15}=3:1[/tex]

Therefore ratio of y and 12 is equal to 3 : 1

Or ratio of 12 to y is 1 : 3

Option B is the answer.

erinna erinna · Answer 2 · 2019-11-04T11:29:57+01:00

Answer:

Option 2.

Step-by-step explanation:

In the figure below, the segment is parallel to one side of the triangle.

Given: BC║DE

In triangle ABC and ADE,

[tex]\angle BAC\cong \angle DAE[/tex] (Reflexive property)

[tex]\angle ABC\cong \angle ADE[/tex] (Corresponding angles)

By AA property of similarity,

[tex]\triangle ABC\sim \triangle ADE[/tex]

Corresponding parts of similar triangle are proportional.

[tex]\frac{DE}{AB}=\frac{AD}{AB}[/tex]

[tex]\frac{12}{y}=\frac{15}{15+30}[/tex]

[tex]\frac{12}{y}=\frac{15}{45}[/tex]

[tex]\frac{12}{y}=\frac{1}{3}[/tex]

The ratio of 12 to y is 1:3. Therefore, the correct option is 2.