Question

The length of the side of a right angle triangle are measured as three consecutive even number find the value of these sides

Answer 1

Answer:

10,8,6 are sides of triangle

Step-by-step explanation:

Let the sides be 2x-2, 2x and 2x+2

Now, The triangle is right angled. So, Pythagoras Theorem can be applied here.

We also know that Hypotenuse is always greater then Perpendicular and Base.

So, Hypotenuse(H)=2x+2

Now, perpendicular and base can be any of the two, that is 2x-2 or 2x

So, let Perpendicular(P)=2x

and Base=2x-2

By Pythagoras theorem,

$H^2=P^2 + B^2$

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

(using  $(a+b)^2=a^2+b^2+2ab$  and $(a-b)^2=a^2+b^2-2ab$)

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

(Taking all the variable in RHS and constants in LHS)

= $0 = 4x^2 - 16x$

= $4x^2 - 16x =0$

= $4x(x-4)=0$

so either

4x=0         or           x-4 = 0

=x=0                        = x=4

But x cant be 0 as then

Base = 2x-2 = 2(0) -2= 0-2= -2

but base is a length which can't be negative

So, x= 4

then Hypotenuse= 2x+2 = 2(4) +2 = 8+2 = 10

Perpendicular = 2x = 2(4) = 8

Base = 2x-2 = 2(4)-2 = 6

So, Answer is 10, 8, 6

Hope you got this :-))

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