Question

For the triangles to be similar by the SSS similarity theorem, what must be the value of y?

Answer 1

Since the triangles are similar, there must be a proportion between them.
This proportion can be found by dividing corresponding sides from each other.
RP and CA are corresponding.  28/14 is 2.  
That means that 2(CB) is RQ.  2(10) is 20.
y is 20.

Answer 2

The value of the side y of triangle PQR is $\boxed{y = 20}$ Option B is correct.

Further  explanation:

The similar triangles are those in which all the corresponding angles are equal and the sides are proportional.

There are many similarity rules and are as follows.

1. Angle Angle Angle (AAA)

2. Side Side Side (SSS)

3. Side Angle Side (SAS)

Given:

The side AB is equal to side BC.

${\text{AB = BC}}$

The side AC is equal to 14.

The side PR is equal to 28.

Explanation:

The triangle ABC is similar to triangle PQR.

Therefore, the corresponding side of triangle ABC and triangle PQR are proportional.

$\dfrac{{{\text{AC}}}}{{{\text{PR}}}}{\text{ = }}\dfrac{{{\text{BC}}}}{{{\text{QR}}}}{\text{ = }}\dfrac{{{\text{AB}}}}{{{\text{PQ}}}}.$

$\begin{aligned}\frac{14}{28}&=\frac{10}{\text{QR}}\\ \frac{1}{2}&=\frac{10}{\text{QR}}\\ \text{QR}&=10\times 2\\\text{QR}&=20\end{aligned}$

The value of the side y of triangle PQR is $\boxed{y = 20}.$

Option A is not correct

Option B is correct

Option C is not correct

Option D is not correct

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Triangle

Keywords: congruent, angles, triangle, ASA, angle side angle, congruent sides, acute angle, side, corresponding angles, congruent triangle.