In triangle PQR, angle q=90 degree. If PQ=12 cm and PR=13 cm find the area of triangle PQR
Posted by: Siddhangana D. on 26.08.2020
Ask a QuestionGiven, PQR is a triangle and <Q =90 degree
And PQ = 12 cm
PR = 13 cm
We know that the area of right angle triangle = 1/2 ( product of legs)
But one leg QR is not given here
So by Pythagores theorem
(PQ)^2 + (QR)^2 = (PR)^2
= (12)^ + (QR)^2 = (13)^2
= 144 + (QR)^2 =169
So, (QR)^2= 169-144
or, (QR)^2=25
so, QR = 5 cm
Now Area of right anged triangle PQR= 1/2 X 5 X 12
=30 sq.cm Answer
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Answer: 5,12&13 form a pythagorean triplets.Given PR=13 cms amd PQ= 12 cms it follows that side
QR of the triangle =5cms. As PR =13 cms is the hypotenuse , the other two are the sides
Therfore the area of the triangle PQR = 1/2*PQ*QR =1/2*12*5= 30 Sq.cm
Applying Pythagoras theorem, QR= root(PR^2 - PQ^2) = root(13^2 - 12^2) cm = root(25) cm = 5 cm .
Hence, area of triangle PQR = (1/2).PQ.QR = (1/2).12.5 cm^2 = 30 cm^2 . (Ans.)
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By using 1/2 *BASE*HIEGHT formula we can find area of triangle but, We know about only two sides so, first we have to find the 3rd side i.e. QR(base) Lest assume QR = a cm
Applying Pythaagoras Theorem.
Third side will be 5cm.
So area = 1/2 * 5 * 12 = 30 square cm.
Get 5 credit points for each correct answer. The best one gets 25 in all.
