Question

The lengths of a right-angled triangle are (x+2) cm, (5x – 1) cm and 5x cm.

Answer 1

SOLUTION

given that sides of right triangle are

( x + 2 ) cm ; ( 5 x -1 ) cm and 5 x  cm

here , the value of x should be positive because if x will be negative or zero then , side ( 5 x - 1 ) , ( 5 x ) will become negative / zero ; that is not possible hence,

in these given three sides when x is positive ; 5x will the largest side means hypotenuse of right angled triangle.

so,

using Pythagorean theorem

( 5 x )² = ( x + 2 )² + ( 5 x - 1 ) ²

25 x² = x² + 4 + 4 x + 25 x² + 1 - 10 x

( 25 x² will be cancelled being on both sides , so )

x² - 6 x + 5 = 0

x² - x ( 5 + 1 ) + 5 = 0

x² - 5x - x + 5 = 0

x ( x - 5 ) - 1 ( x - 5 ) = 0

(x - 1 ) ( x - 5 ) = 0

x = 1   and  x = 5

so, taking x = 1

sides of triangle will be

( x + 2 ) = ( 1 + 2 ) = 3 cm

( 5 x - 1 ) = ( 5(1) - 1 ) = 4 cm

5 x = 5 (1) = 5 cm

and , taking x = 5

sides will be

( x + 2 ) = ( 5 + 2 ) = 7 cm

( 5 x - 1 ) = ( 5 (5) - 1 ) = 24 cm

5 x = 5 (5) = 25 cm.

Answer 2

If u want the CMs then use this trick

THE PYTHOGOROUS THEOREM.

$a ^{2} + b ^{2} = c ^{2}$

2(x+2)+2(5x-1)=2(5x)

2x+4+10x-2=10x

2x+10x-10x=-4+2

2x =2

x=2/2

x=1

We found it ,

now substituting x=1.

A= (x+2)

=1+2

A =3cm

B=5x-1

=5(1)-1

=5-1

B =4cm

C=5x

=5(1)

C=5cm