Question

# R and S are midpoints of sides XZ and ZY, respectively, of sides of a triangle ZYX. Find the perimeter of triangle ZYX.

- 72
- 32
- 36
- 66

Hint:

### If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

## The correct answer is: 32

### Triangle ZSR is similar to triangle ZYX

Hence, the correct option is A.

Perimeter= Sum of all sides.

### Related Questions to study

### AB = x + 5, BD = 12, AC = 3x + 1, and CF = 15. Find the value of *x* if ABC is a triangle and BC ll DF.

It is also called basic proportionality theorem.

### AB = x + 5, BD = 12, AC = 3x + 1, and CF = 15. Find the value of *x* if ABC is a triangle and BC ll DF.

It is also called basic proportionality theorem.

### Find the length of AC.

It is also called basic proportionality theorem.

### Find the length of AC.

It is also called basic proportionality theorem.

### Find the value of *z.*

It is also called basic proportionality theorem.

### Find the value of *z.*

It is also called basic proportionality theorem.

### If KM ll JN, then find the value of J.

It is also called basic proportionality theorem.

### If KM ll JN, then find the value of J.

It is also called basic proportionality theorem.

### In the figure, DE ll AB and If CE = t – 2, EB = t + 1, CD = 2, and CA = 10, find *t.*

It is also called basic proportionality theorem.

### In the figure, DE ll AB and If CE = t – 2, EB = t + 1, CD = 2, and CA = 10, find *t.*

It is also called basic proportionality theorem.

### The line DE is parallel to AC If BC = 18, BE = 6, DC = 16, and AD = 8.Find EC.

It is also called basic proportionality theorem.

### The line DE is parallel to AC If BC = 18, BE = 6, DC = 16, and AD = 8.Find EC.

It is also called basic proportionality theorem.

### Find the value of ‘a’.

It is called theorem of parallel lines cut by transversals proportionality.

### Find the value of ‘a’.

It is called theorem of parallel lines cut by transversals proportionality.

### If line segment AD is an angle bisector and AB=6, AC = 10, and BD = 3, what must DC equal?

Here, the value of DC is 5.

### If line segment AD is an angle bisector and AB=6, AC = 10, and BD = 3, what must DC equal?

Here, the value of DC is 5.

### Choose the correct statement for the angle bisector theorem to the following triangle.

The base is divided in the same ratio as the sides containing the angle.

### Choose the correct statement for the angle bisector theorem to the following triangle.

The base is divided in the same ratio as the sides containing the angle.

### Theorem used to find the value of AB in the following figure

Here, AB = 4√2.

### Theorem used to find the value of AB in the following figure

Here, AB = 4√2.

### To find the value of AB in the figure, which theorem is used?

If two or more parallel lines are cut by two transversals, then they divide the transversals proportionally.

### To find the value of AB in the figure, which theorem is used?

If two or more parallel lines are cut by two transversals, then they divide the transversals proportionally.

### Which of the statements is true in the case of the given triangle?

The base is divided in the same ratio as the sides containing the angle.

### Which of the statements is true in the case of the given triangle?

The base is divided in the same ratio as the sides containing the angle.

### To find the value of *p, *which statements can be used?

Her, the value of p is 43.5.

### To find the value of *p, *which statements can be used?

Her, the value of p is 43.5.

### In the figure, to find the value of *x* which theorem can be used?

Here, the value of x is 10.

### In the figure, to find the value of *x* which theorem can be used?

Here, the value of x is 10.

It is also called basic proportionality theorem.

It is also called basic proportionality theorem.