Q1 of 27 Page 289

If the followings are the lengths of the three sides of a triangle, then let us write by calculating, the cases where the triangles are right-angled triangles:

8cm., 15cm. and 17 cm.

Given: Three sides of a triangle are 8 cm, 15 cm and 17 cm.


To check if the triangle is a right-angled triangle, we verify by Pythagoras theorem.


Taking the longest side to be hypotenuse and other two sides as base and perpendicular, we have,


Hypotenuse, h = 17 cm


Perpendicular, p = 8 cm


Base, b = 15 cm


According to Pythagoras theorem,


h2 = p2 + b2


⇒ 172 = 82 + 152


⇒ 289 = 64 + 225


⇒ 289 = 289


Hence, verified that the triangle is a right- angled triangle.


More from this chapter

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1

If the followings are the lengths of the three sides of a triangle, then let us write by calculating, the cases where the triangles are right-angled triangles:

9cm., 11cm. and 6cm.

 2

In the road of our locality there is a ladder of 15m. length kept in such a way that it has touched Milli’s window at a height of 9m. above the ground. Now keeping the foot of the ladder at the same point of that road. The ladder is rotated in such a way that it touched our window situated on the other side of the road. If our window is 12m. above the ground, then let us determine the breadth of that road in our locality.

 3

If the length of one diagonal of a rhombus having the side 10cm. length is 12cm., then let us write, by calculating the length of other diagonal.

 4

I have drawn a triangle PQR whose ∠Q is right angle. If S is any point on QR, let us prove that, PS2 + QR2 = PR2 + QS2