Question

Given : In trapezium PQRS,
side PQ || side SR, AR = 5AP,
AS = 5AQ then prove that,
SR = 5PQ​

Answer 1

Answer:

5PQ

Step-by-step explanation:

A trapezium PQRS is drawn in such a way that PQ || RS , AR = 5AP and AS = 5AQ

See In figure, ∵ PQ || RS

∴ ∠PQA = ∠ASR

∠QPA = ∠ARS

And also ∠PAQ = ∠SAR

From A - A - A similarity rule,

∆APQ ~ ∆ARS

∴ PQ/RS = AP/AR = AQ/AS

Given, AR = 5AP so,

PQ/RS = AP/5AP = 1/5

⇒PQ = RS/5

⇒RS = 5PQ or, SR = 5PQ

Hence, proved\bf{SR=5PQ}SR=5PQ