Question

check if following sides make right angled triangle 1) 10cm, 20cm, 11cm 2) 6cm, 8cm, 10cm​

Answer 1

Given -

• 1st sides = 10cm, 20cm and 11cm

• 2nd sides = 6cm, 8cm and 10cm

To find -

• If sides will make a right angled triangle.

Formula used -

• Pythagoras theorem

Solution -

In the question, we are provided with the sides of 2 triangles, and we need to find, will those sides will make, right angled triangle or not. For that we will use Pythagoras theorem. First, we will consider the longest unit as hypotenuse and and then, we will do the square of hypotenuse and the other two sides. Then we will add up the square of two sides, and will see if it is, equal to the square of hypotenuse, if yes, then it will make a right angled triangle, if not, then it will not make. Let's do it!

For 1st sides -

20cm = Hypotenuse or H

10cm = Side A

11cm = Side B

Pythagoras theorem = (H)² = (A)² + (B)²

Where -

H = Hypotenuse

A = 1st side

B = 2nd side

On substituting the values -

$\bf \: {(20)}^{2} = {(10)}^{2} + {(11)}^{2} \\ \\ \bf \: 400 \: = 100 \: + \: 121 \\ \\ \bf \: 400 \: \neq \: 221$

$\therefore$ 10cm, 20cm and 11cm will not make a right - angled triangle.

Now for 2nd sides -

10cm = Hypotenuse Or H

8cm = Side A

6cm = Side B

Pythagoras theorem = (H)² = (A)² + (B)²

Where -

H = Hypotenuse

A = 1st side

B = 2nd side

On substituting the values -

$\bf \: {(10)}^{2} = {(8)}^{2} + {(6)}^{2} \\ \\ \bf \: 100 = 64 + 36 \\ \\ \bf \: 100 = 100$

$\therefore$ 10cm, 8cm and 6cm will make a right angled triangle.

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