Question

in a right triangle ,acute angle is double of the other triangle then the hypotenuse is​

Answer 1

Answer:

ANSWER

Given: A △PRQ in which

∠Q=90

∘

and ∠PRQ=2∠QPR

Const. Produce RQ to S such that

RQ=QS. Join PS.

QS=QR (By construction)

PQ=PQ (Common)

∠PQS=∠PQR (Each=90

∘

)

∴ △PQS≅△PQR (SAS)

⇒ PS=PR and ∠SPQ=∠RPQ (cpct)

Let ∠SPQ=x. Then ∠PRQ=2x (Given)

Then ∠SPR=∠SPQ+∠RPQ

=x+x=2x

⇒ ∠spr=∠prq=SR=PS (Sides opp. equal ∠s are equal)

⇒ 2QR=PS {∵SQ=QR∵SR=2QR}

⇒ 2QR=PR (∵PS=PR)

⇒ The hypotenuse PR is double the smallest side QR.