Question

in triangle abc angle b is 90 degree find the sides of the triangle if ab = 2 x minus 3 cm BC = 2 X + 4 cm and ac is equal to X + 6​

Answer 1

Answer:

For right angle triangle

by Pythagoras theorem

ab^2 + bc^2 = ac^2

(x-3)^2 + (x+4)^2 = (x+6)^2

x^2 -6x +9 + x^2 + 8x + 16 = x^2 + 12x + 36

2x^2 +2x + 25 = x^2 + 12x + 36

x^2 -10x -11 = 0

x = (-b+-√(b^2 -4ac))/2a

x = {-(-10) +- √(100+44)}/2

=(10 +- √144)/2

= (10 +- 12)/2

x=(10+12)/2 or x = (10 -12)/2

x= 22/2 or x = -2/2

x =11 or x = -1

since side cannot be negative

so x = 11

there fore sides of triangle are

x-3 = 11-3=8

x+4=11+4=15

x+6=11+6=17

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Answer 2

Answer:

We are given, m∠B=90

o

AB=(x−3) cm

BC=(x+4) cm

AC=(x+6) cm

x=?

From pythagoras theorem,

AC

2

=AB

2

+BC

2

(x+6)

2

=(x−3)

2

+(x+4)

2

∴ x

2

+12x+36=x

2

−6x+9+x

2

+8x+16

∴ x

2

+12x+36=2x

2

+2x+25

∴ 2x

2

−x

2

+2x−12x+25−36=0

∴ x

2

−10x−11=0

∴ x

2

−11x+x−11=0

∴ x(x−11)+1(x−11)=0

∴ (x+1)(x−11)=0

So, x+1=0 or x−11=0

x=−1

or

x=11