Question 774214
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Since it is a right triangle, we can apply the Pythagoras theorem
Square of hypotenuse = square of leg1 + square of leg2.
{{{(x + 4)^2 = x^2 + (x + 2)^2}}}
Expanding the Left and right sides
{{{x^2 + 8*x + 16 = x^2 + x^2 + 4*x + 4 = 2*x^2 + 4*x + 4}}}
Moving all terms to one side
{{{2*x^2 - x^2 + 4*x - 8*x + 4 - 16 = 0}}}
{{{x^2 - 4*x - 12 = 0}}}
This is a standard quadratic equation which can b solved by factorization
{{{x^2 - 6*x + 2*x - 12 = 0}}}
{{{x*(x - 6) + 2*(x - 6) = 0}}}
{{{(x + 2)*(x - 6) = 0}}}
The two roots (solutions) for x are
x + 2 = 0 or x = -2
x - 6 = 0 or x = 6
Take only the positive value of the x.
So one leg of the triangle is 6
The other leg is (6 + 2) or 8.
The hypotenuse is (6 + 4) or 10.
The sides of the triangle are 6, 8 and 10 units.
Hope you got it :)
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