Question

the longest side of a right angled triangle is 4cm longer than the one side and 2cm longer than the other side. find the longest side

Answer 1

let longest side of right angeled triangle be x

therefore one remained side = x -4

other remained side = x-2

now ,
we know that in right Angeles triangle ,
longest side is hypotenuse

by using Pythagoras theorem

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

x^2 -4x+4 + x^2 - 8x +16 = x^2

2x^2 -12x + 20 = x^2

x^2 -12x + 20 = 0

x^2 -10x -2x + 20 = 0

x(x-10) - 2( x-10) = 0

(x-10) (x-2) = 0

x-10 =0 or x-2 = 0

x =10 or x = 2

but x =2 can not be possible

therefore x = 10 which is longest side

other sides are
10 -2 =8
10 -4 = 6

Answer 2

Answer:

Let longest side of right angled triangle be x

therefore one remained side = x-4

other remain side =x-2

Now,

Step-by-step explanation:

we know that in, right Angeles triangle, longest side is hypotenus

by using Pythagoras theorem

$(x - {2) }^{2} + (x - 4 {)}^{2} = x {}^{2}$

${x}^{2} - 4x + 4 + {x }^{2} - 8x + 16 = {x}^{2}$

$2x {}^{2} - 12x + 20 = {x}^{2}$

${x}^{2} - 12x + 20 = 0$

${x}^{2} - 10x - 2x + 20 = 0$

$x(x - 10) - 2(x - 10) = 0$

$(x - 10)(x - 2) = 0$

$x - 10 = 0 \: \: or \: \: x - 2 = 0$

$x = 10 \: \: or \: \: x = 2$

$but \: x = 2 \: can \: not \: be \: possible$

$therefore \: x = 10 \: which \: is \: longest \: side \:$

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