Question

Which of the following can be side of a right triangle?Solve it.

(a) 8 cm, 15 cm, 17 cm
(b) 3 cm, 3 cm, 9 cm
(c) 2.5 cm, 6.5 cm, 6 cm
(d) 16 cm, 30 cm, 34 cm

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Answer 1

Answer :-

• Option a, option c and option d can be the sides of a right angled triangle.

Solution :-

• First let's understand the trick to solve questions like this.

Lets understand!

• In this question, we will use the Pythagoras theorem to find out which of the following measures can be those of a right angled triangle.

First let's see what is Pythagoras theorem and what are it's rules.

We know that :-

• If the Pythagoras theorem holds for some triangle, then it is a right angled triangle.

So, to find out which of the following measures is that of a right angled triangle, we have to check whether these measures satisfy the Pythagoras theorem or not.

What is the Pythagoras theorem?

In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other sides. This is the Pythagoras theorem. It was discovered by Pythagoras, a Greek philosopher of sixth century B.C.

What is hypotenuse?

In a right angled triangle, the sides have special names. The side opposite to the right angled triangle is called hypotenuse. Hypotenuse is the longest side.

• The measures which will satisfy this theorem can be the sides of a right angled triangle.

So let's check all the options one by one.

Step-by-step explanation :-

Since we know all the formulas and the rules, therefore let's check all the options using them.

Option a.

a) 8 cm, 15 cm, 17 cm.

The longest side = 17 cm.

So, 17 cm is the hypotenuse.

By Pythagoras theorem,

8² + 15² should be equal to 17².

LHS

$\Rightarrow$ 8² + 15²

$\Rightarrow$ 64 + 225

$\Rightarrow$ 289 cm.

RHS

$\Rightarrow$ 17²

$\Rightarrow$ 289 cm.

LHS = RHS,

Since they satisfy the Pythagoras theorem,

Therefore, these measures can be the sides of a right angled triangle.

Option b.

b) 3 cm, 3 cm, 9 cm.

The longest side = 9 cm.

So, 9 cm is the hypotenuse.

By Pythagoras theorem,

3² + 3² should be equal to 9².

LHS

$\Rightarrow$ 3² + 3²

$\Rightarrow$ 9 + 9

$\Rightarrow$ 18 cm.

RHS

$\Rightarrow$ 9²

$\Rightarrow$ 81 cm.

LHS ≠ RHS,

Since they don't satisfy the Pythagoras theorem,

Therefore, these measures can't be the sides of a right angled triangle.

Option c.

c) 2.5 cm, 6.5 cm, 6 cm.

The longest side = 6.5 cm.

Therefore, 6.5 cm is the hypotenuse.

By Pythagoras theorem,

2.5² + 6² should be equal to 6.5².

LHS

$\Rightarrow$ 2.5² + 6²

$\Rightarrow$ 6.25 + 36

$\Rightarrow$ 42.25 cm.

RHS

$\Rightarrow$ 6.5²

$\Rightarrow$ 42.25 cm.

LHS = RHS,

Since they satisfy the Pythagoras theorem,

Therefore, these measures can be the sides of a right angled triangle.

Option d.

d) 16 cm, 30 cm, 34 cm.

The longest side = 34 cm.

Therefore 34 cm is the hypotenuse.

By Pythagoras theorem,

16² + 30² should be equal to 34².

LHS

$\Rightarrow$ 16² + 30²

$\Rightarrow$ 256 + 900

$\Rightarrow$ 1156 cm.

RHS

$\Rightarrow$ 34²

$\Rightarrow$ 1156 cm.

LHS = RHS,

Since they satisfy the Pythagoras theorem,

Therefore, these measures can be the sides of a right angled triangle.

Therefore, the measures given in option a, option c and option d can be the sides of a right angled triangle.