Question

If the lengths of the perineter and the hypotenuse of a right- angled triangle is 60 cm. and 26 cm.,then the length of one of its sides must be

यदि किसी समकोण त्रिभुज के परिमाप व कर्ण की लम्बाई 60 cm. व 26 cm. हो, तो उसके एक पाद की लम्बाई होनी
चाहिये :
(1) 14cm
(2) 20 cm
(3) 24 cm
(4) 22 cm​

Answer 1

Answer :

The correct option is :

(3) 24cm

When the base is 10cm , perpendicular is 24cm

and when base is 24cm , perpendicular is 10cm

Given :

• The perimeter of the right angled triangle is 60cm
• The length of the hypotenuse of the triangle is 26cm

To Find :

• The other sides of the triangle

Formulae Used :

• Sum of all the sides of triangle = perimeter of the triangle
• Base² + Perpendicular² = hypotenuse²

Solution :

Let us consider the other two sides of the triangle be x and y

Given ,

Perimeter of triangle = 60cm

$\sf{\implies x + y + 26cm = 60cm}\\ \sf{\implies x + y = 60cm - 26cm}\\ \sf{\implies x + y = 34cm}\\ \sf{\implies y = 34 - x}$

Now by Pythagorean theorem we have :

$\sf{base^{2} + perpendicular^{2} = hypotenuse^{2} }\\ \sf{\implies x^{2} + (34 - x)^{2}= 26^{2}}\\ \sf{\implies x^{2}+x^{2} - 68x + 34^{2} = 26^{2} }\\ \sf{\implies 2x^{2} -68x + 1156 = 676}\\ \sf{\implies 2x^{2} - 68x + 1156 - 676 = 0}\\ \sf{\implies 2x^{2} -68x + 480 = 0}\\ \sf{\implies x^{2} - 34x + 240= 0}\\ \sf{\implies x^{2} - 10x - 24x + 240 = 0 } \\ \implies \sf{x(x - 10) - 24(x - 10) =0}\\ \implies\sf{(x - 10)(x - 24)}$

Now we have :

x - 10 = 0 or x - 24 = 0

→ x = 10 or →x = 24

Thus one side is either 10cm or 24cm

since the other side is :

y = 34 - x

so

y = 34 - 10 or y = 34 - 24

→ y = 24cm or → y = 10cm

Thus , the other side is either 24cm or 10cm

Answer 2

...

$\tt{\huge{\purple{ ..................... }}}$

QUESTION -

If the lengths of the perineter and the hypotenuse of a right- angled triangle is 60 cm. and 26 cm.,then the length of one of its sides must be ...........

यदि किसी समकोण त्रिभुज के परिमाप व कर्ण की लम्बाई 60 cm. व 26 cm. हो, तो उसके एक पाद की लम्बाई होनी चाहिये :...

(1) 14cm.

(2) 20 cm.

(3) 24 cm.

(4) 22 cm

SOLUTION :

From the above Question -

We can gather the following information....

If the lengths of the perineter and the hypotenuse of a right- angled triangle is 60 cm. and 26 cm.

Let the sides it's the required right angled Triangle be a , b and √ a ^ 2 + b ^ 2 .

Now,

a + b = 60 cm - 26 cm = 34 cm.

Now,

In option A :

a = 14 cm

=> b = 20 cm

√ { a ^ 2 + b ^ 2 } Not equal to 26 cm

In Option B :

a = 20 cm

=> b = 14 cm

√ { a ^ 2 + b ^ 2 } Not equal to 26 cm

Option c :

a = 24 cm

b = 10 cm

√ { a ^ 2 + b ^ 2 } = 25 cm.

Have option C is correct Option.....