(i) 2.5 cm, 6.5 cm, 6 cm.

(ii) 2 cm, 2 cm, 5 cm.

(iii) 1.5 cm, 2 cm, 2.5 cm

Answer :

(i) Given sides are 2.5 cm, 6.5 cm, 6 cm.

Square of the longer side = \((6.5)^2 = 42.25 \) cm.

Sum of the square of other two sides
= \( (2.5)^2 + (6)^2 = 6.25 + 36 \)
= 42.25 cm.

Since, the square of the longer side in a triangle is equal to the sum of the squares of other two sides.

\(\therefore \)The given sides form a right triangle.

(ii) Given sides are 2 cm, 2 cm, 5 cm .

Square of the longer side =\( (5)^2 = 25 \)cm

Sum of the square of other two sides
=\( (2)^2 + (2)^2 =4 + 4 = 8 cm \)
Since 25 cm \(\neq \)8 cm

\(\therefore \)The given sides do not form a right triangle.

(iii) Given sides are 1.5 cm, 2 cm, 2.5 cm

Square of the longer side = \( (2.5)^2 = 6.25 \)cm

Sum of the square of other two sides
= \((1.5)^2 + (2)^2 = 2.25 + 4 = 6.25cm = 6.25 cm = 6.25 cm \)

Since the square of longer side in a triangle is equal to the sum of square of other two sides.

\(\therefore \)The given sides form a right triangle.

- Q.1 PQR is a triangle, right-angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
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- Q.3 A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
- Q.5 A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree . Find the original height of the tree.
- Q.6 Angles Q and R of a APQR are 25° and 65°. Write which of the following is true. (i) \( PQ^2 + QR^2 = RP^2 \) (ii)\( PQ^2 + RP^2 = QR^2 \) (iii)\( RP^2 + QR^2 = PQ^2 \)
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- NCERT solutions for class 7 maths chapter 3 Data Handling
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