Question

the hypotenuse of a right angled triangle is 26cm and the sum of the other two sides is 34cm. Find the length of its sides

Answer 1

Hey mate !!

Here's the answer !!

Let the two sides be x and y

It is given that, x + y = 34 cm.

=> y = 34 - x   -----( 1 )

We know that ,

Sum of square of sides = Hypotenuse square

=> x² + ( 34 - x )² = 26²

=> x² + ( 1156 - 68x + x² ) = 676

=> x² + x² - 68x + 1156 = 676

=> 2x² - 68x + 1156 - 676 = 0

=> 2x² - 68x + 480 = 0

Dividing by 2 throughout the equation, we get,

=> x² - 34x + 240 = 0

=> x² - 24x - 10x + 240 = 0

=> x ( x - 24 ) - 10 ( x - 24 ) = 0

=> ( x - 10 ) ( x - 24 ) = 0

=> x = 10, 24

If x = 10 then other side is 34 - 10 = 24

If x = 24 then other side is 34 - 24 =10

Hence the other two sides of the triangle are 24 units and 10 units with hypotenuse of 26 units.

Hope my answer helps !!

Cheers !!

Answer 2

Hey friend !!

here's your solution :-

\______________________/

Given that ,

In a right angle triangle :-

Hypotenuse = 26 cm

Sum of the other two sides = 34 cm

Length of the side = ?

_______________________

Let the other two sides be " x " nd " y "

According to the question ,

Sum of the other two sides = 34 cm

===》x + y = 34 cm

===》x = 34 - y .................( 1 )

As we know that ,

==> h ^2 = a ^2 + b ^2

==> 26 ^2= a^ 2 + ( 34 - y )^2

==> 676 = y ^2 + ( 1156 + y ^2 - 68y )

==> 676 = y ^2 + y ^2 - 68y + 1156

==> 2 y^2 - 68y + 1156 - 676 = 0

==> 2 y^2 - 68y + 480 = 0

OR

==> y ^2 - 34y + 240

On factorization :-

==> y ^2 - 24 y - 10y + 240.

==> y ( y - 24 ) - 10 ( y - 24 )

( y - 10 ) ( y - 24 )

Hence the value of y is :-

■ ( y - 10 ) = 0

==> y = 10

■ ( y - 24 )

==> y = 24

Put the values of " y " on eq. ==》

■ x + y = 34

1 ) x = 34 - 24

=====》10

Put the value of " x "

■ x + y = 34

=> 10 + y = 34

=> y = 24

_________________________

Hence the value of " x " And " y " respectively 10 nd 24

_________________________

hope it helps !

thanks for asking :)

☆ be brainly ☆