Question

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

Answer 1

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,

$\angle BAC\cong \angle DAE$               (Reflexive property)

$\angle ABC\cong \angle ADE$                (Corresponding angles)

By AA property of similarity,

$\triangle ABC\sim \triangle ADE$

Corresponding parts of similar triangle are proportional.

$\frac{DE}{AB}=\frac{AD}{AB}$

$\frac{12}{y}=\frac{15}{15+30}$

$\frac{12}{y}=\frac{15}{45}$

$\frac{12}{y}=\frac{1}{3}$

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

Answer 2

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.

$\frac{AB}{ED}=\frac{AC}{EC}$

$\frac{y}{12}=\frac{30+15}{15}=\frac{45}{15}=3:1$

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.