Question

in triangle PQR, PQ:QR : RP = 3 :4 : 5 prove that the triangle is right angle


answer is 90° how​

Answer 1

Answer:

Yes it is right angle

Step-by-step explanation:

3+4+5=12. 3÷12×90=22.5, 4÷12×90=30,. 5÷12×90=37.5° , 22.5+30+37.5=90°

Answer 2

Answer :

ΔPQR is a right angled triangle.

Step-by-step explanation :

Given,

In ΔPQR , PQ : QR : RP = 3 : 4 : 5

Let

• PQ = 3x
• QR = 4x
• RP = 5x

Longest side is 5x

Square of the longest side,

RP² = (5x)²

RP² = 25x²

Now, sum of the squares of the remaining sides is

PQ² + QR²

= (3x)² + (4x)²

= 9x² + 16x²

= 25x²

Since, the square of the longest side is equal to the sum to the squares of the remaining sides

i.e., RP² = PQ² + QR²

ΔPQR is a right angled triangle.

Hypotenuse = 5x  (longest side)

Hypotenuse = RP

The angle opposite to the hypotenuse is right angled.

∴ ∠PQR = 90°