Question

In the diagram, the length of segment TQ is 40 units.

What is the length of segment QV?

Answer 1

D (44)

Explanation:

Quiz edge 2020

Answer 2

Answer: The length of segment QV is 44 units.

Explanation:

Consider Δ STR and ΔQTR,

∠TRQ = ∠TRS = 90°

TR = TR (Common)

SR = RQ (Given)

So, ΔTSR ≅ ΔTQR ( By SAS Congruence Criterion)

So, By CPCT (Correspondence part of congruent triangle)

TS = TQ

`2x+8=40\\\\2x=40-8\\\\2x=32\\\\x=(32)/(2)\\\\x=16`

similarly, ΔSVR ≅ ΔQVR

so, SV = QV

`QV=3x-4=3* 16-4=48-4=44\ units`

Hence, the length of segment QV is 44 units.