Question

Look at the figure shown below:

A triangle RPQ is shown. S is a point on side PR and T is a point on side PQ. Points S and T are joined using a straight line. The length of PS is equal to 60, the length of SR is equal to x, the length of PT is equal to 48 and the length of TQ is equal to 36.

Nora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 45.


Statement Reason
1. Segment ST is parallel to segment RQ Given
2. Angle QRS is congruent to angle TSP Corresponding angles formed by parallel lines and their transversal are congruent
3. Angle SPT is congruent to angle RPQ Reflexive property of angles
4. Triangle SPT is similar to triangle RPQ Angle-Angle Similarity Postulate
5. 60: (60+x) = Corresponding sides of similar triangles are in proportion

Which of the following can she use to complete statement 5?
60:(48 + 36)
60:36
48:36
48:(48 + 36)

Answer 1

I think she can use 48:(48+36)

Answer 2

The Answer is
`(48)/(48+36)`

Explanation:

Let me draw this triangle for you as you haven't drawn the triangle.

To find the side SR , you have shown that

ΔPST ~(is similar to)ΔPRQ [AA]

As, you know when triangles are similar their sides are proportional.

So,
`(60)/(60+x)=(48)/(48+36)\\(60)/(60+x)=(48)/(84)\\(60)/(60+x)=(4)/(7)\\240 +4x=420\\4x=420-240\\4x =180\\x=45`

You can solve this question using other way also

As, ST║RQ

then
`(PS)/(SR)=(PT)/(TQ)`⇒ [ if in a triangle a line is parallel to a side

intersecting the other two sides in distinct points then the ratio of the segments where the line segment intersects the other two sides are same.]

`(48)/(36)=(60)/(x)\\</p><p>x=45`