Question

which of the following can be the sides of a right-angled triangle?
15cm, 32cm, 57cm
65cm, 72cm, 97cm
20cm, 21cm, 31cm
35cm, 77cm, 88cm​

Answer 1

EXPLANATION.

Right angled triangle.

As we know that,

In right angled triangle,

⇒ H² = P² + B².

Hypotenuse is  equal to sum of their base and perpendicular sides, we get.

Always take biggest length as hypotenuse.

Their order,

Hypotenuse > perpendicular > base.

(1) = 15cm, 32cm, 57cm,

Hypotenuse = 57cm

Perpendicular = 32cm

base = 15cm.

⇒ H² = P² + B².

⇒ (57)² = (32)² + (15)².

⇒ 3249 = 1024 + 225.

⇒ 3249 = 1249.

⇒ 3249 ≠ 1249

It is not a right angled triangle.

(2) = 65cm, 72cm, 97cm.

Hypotenuse = 97cm.

Perpendicular = 72cm.

Base = 65cm.

⇒ H² = P²+ B².

⇒ (97)² = (72)² + (65)².

⇒ 9409 = 5184 + 4225.

⇒ 9409 = 9409.

It is a right angled triangle.

(3) = 20cm, 21cm, 31cm.

Hypotenuse = 31cm.

Perpendicular = 21cm.

Base = 20cm.

⇒ H² = P² + B².

⇒ (31)² = (21)² + (20)².

⇒ 961 = 441 + 400.

⇒ 961 = 841.

⇒ 961 ≠ 841.

It is not a right angled triangle.

(4) = 35cm, 77cm, 88cm.

Hypotenuse = 88cm.

Perpendicular = 77cm.

Base = 35cm.

⇒ H² = P² + B².

⇒ (88)² = (77)² + (35)².

⇒ 7744 = 5929 + 1225.

⇒ 7744 = 7154.

⇒ 7744 ≠ 7154.

It is not a right angled triangle.

Option [B] is a correct answer.

Answer 2

Answer:

Question :-

➦ Which of the following can be the sides of a right angled triangle ?

1) 15 cm , 32 cm , 57 cm

2) 65 cm , 72 cm , 97 cm

3) 20 cm , 21 cm , 31 cm

4) 35 cm , 77 cm , 88 cm

Solution :-

As we know that,

✯ (Hypotenuse)² = (Perpendicular)² + (Base)² ✯

1) 15 cm , 32 cm , 57 cm

We know that, Hypotenuse is the largest side.

Given :

• Hypotenuse = 57 cm
• Perpendicular = 32 cm
• Base = 15 cm

According to the question by using the formula we get,

⇒ (57)² = (32)² + (15)²

⇒ 57 × 57 = 32 × 32 + 15 × 15

⇒ 3249 = 1024 + 225

⇒ 3249 = 1249

➠ 3249 ≠ 1249

Pythagoras theorem is not satisfied.

Hence, 15 cm , 32 cm , 57 cm does not form the side of a right angled triangle.

_____________________

2) 65 cm ,72 cm , 97 cm

We know that,

✧ (Hypotenuse)² = (Perpendicular)² + (Base)² ✧

We know that, Hypotenuse is the largest side.

Given :

• Hypotenuse = 97 cm
• Perpendicular = 72 cm
• Base = 65 cm

According to the question by using the formula we get,

⇒ (97)² = (72)² + (65)²

⇒ 97 × 97 = 72 × 72 + 65 × 65

⇒ 9409 = 5184 + 4225

⇒ 9409 = 9409

➠ 9409 = 9409

Pythagoras theorem is satisfied.

Hence, 65 cm , 72 cm , 97 cm form the side of a right angled triangle.

_______________________

3) 20 cm , 21 cm , 31 cm

As we know that,

✪ (Hypotenuse)² = (Perpendicular)² + (Base)² ✪

We know that, Hypotenuse is the largest side.

Given :

• Hypotenuse = 31 cm
• Perpendicular = 21 cm
• Base = 20 cm

According to the question by using the formula we get,

⇒ (31)² = (21)² + (20)²

⇒ 31 × 31 = 21 × 21 + 20 × 20

⇒ 961 = 441 + 400

⇒ 961 = 841

➠ 961 ≠ 841

Pythagoras theorem is not satisfied.

Hence, 20 cm , 21 cm , 31 cm does not form the side of a right angled triangle.

_______________________

4) 35 cm , 77 cm , 88 cm

As we know that,

★ (Hypotenuse)² = (Perpendicular)² + (Base)² ★

We know that, Hypotenuse is the largest side.

Given :

• Hypotenuse = 88 cm
• Perpendicular = 77 cm
• Base = 35 cm

According to the question by using the formula we get,

⇒ (88)² = (77)² + (35)²

⇒ 88 × 88 = 77 × 77 + 35 × 35

⇒ 7744 = 5929 + 1225

⇒ 7744 = 7154

➠ 7744 ≠ 7154

Pythagoras theorem is not satisfied.

Hence, 35 cm , 77 cm , 88 cm does not form the side of a right angled triangle.

______________________

Hence, correct options is option no (2).

65 cm , 72 cm , 97 cm