Question

length of two sides of a right triangle containing the right angle differ by 2cm .area is 24cm find its perimeter

Answer 1

perimeter is also 24

Answer 2

let the sides be x and (x+2)

Area of right angled triangle = height ×base/2

24*2 = x ×(x+2)

$x^2 +2x = 48$

$x^2 + 2x - 48 = 0$


$x^2 + (8-6)x - 48 =0$


$x^2 + 8x - 6x - 48 = 0$


$x(x+8) - 6(x+8) = 0$

$(x+8) (x-6) = 0$

x = -8  Or x = 6   [zero product rule]

x = 6 [taking positive value]

Now,

sides are 

6 and (6+2) = 8 

Now,

By pythagoras theorem,

$6^2 + 8^2 = hypotenuse^2$

36 + 64 = hypotenuse^2

100 = $hypotenuse^2$

$\sqrt{100} = hypotenuse$

10 = hypotenuse 

Now,


perimeter = 6+8 + 10

Perimeter = 24 cm



i hope this will help you


-by ABHAY