Question

the sides of a right
angled triangle are xcm ,4(x+1),
& (4x+5) cm. Find x​

Answer 1

By Pythagoras theorem

H²=P²+B²

(4x+5)²= x²+(4x+3)²

16x²+25+20x = x² +16x² +9+12x

25+20x -9-12x-x²=0

16+8x-x²=0

x²-8x-16=0

a= 1 ,b= -8, c= -16

D= b²-4ac= 64-64 = 0

x= -b +- √D /2a = 8+- 0/2 = +- 8/2 = +- 4

x= 4 and x=-4

Answer 2

given

Right angle triangle

sides of triangle- xcm ,4(x+1),

& (4x+5) cm.

To find

Find x

solution

Pythagoras theorem:

▪️In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two

Apply phythagoras Theorem

x²+ (4x+4)²= (4x+5)²

x² + 16x²+16 + 32x= 16x² +25 + 40x

x²- 16x²+ 16x²+ 16-25 +32x- 40x = 0

x²- 8x -9= 0

x²- 9x+x-9 = 0

x(x-9) +1(x-9)=0

(x+1) (x-9) = 0

x= -1 , 9

since the side of triangle cannot be negative so

x= 9 cm

-----------------------------------------------------------