if ∆ PQR is right angled at Q and PQ= QR. if QS is perpendicular to PR and QS is = 4 cm then the perimeter of ∆PQR =
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if ∆ PQR is right angled at Q and PQ= QR. if QS is perpendicular to PR and QS is
if ∆ PQR is right angled at Q and PQ= QR. if QS is perpendicular to PR and QS is = 4 cm then the perimeter of ∆PQR =
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Answer:
Given, ΔPQR in which ∠Q = 90°, QS ⊥ PR and PQ = 6 cm, PS = 4 cm In ΔSQP and ΔSRQ,
Given:
∆ PQR is right-angled at Q and PQ= QR.
To find:
The perimeter of ∆ PQR
Solution:
Let the side of the triangle PQ=QR is x cm
As the given triangle is a right-angled triangle Then by the Pythagoras theorem
we get the length of the side PR as x√2 cm
As the line perpendicular to the hypotnues of the triangle is of length 4 cm;
So by the property of the right angled triangle that line must be the bisector of the Hypotnues of the right angled triangle.
So from the Pythagoras Theorem;
As per the assumed sides of the triangle the perimeter is given by:
Hence,
The perimeter of the ∆PQR is 8(√2+1) cm