The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.
Step-by-step explanation:
Let,
Longer leg = a = x
Shorter leg = b = x - 6
Hypotenuse = c = x + 6
As the triangle is right angles, therefore, using pythagoras theorem;
[tex]a^2+b^2=c^2\\(x)^2+(x-6)^2=(x+6)^2\\x^2+(x^2-12x+36)=x^2+12x+36\\x^2+x^2-12x+36=x^2+12x+36\\ 2x^2-12x+36=x^2+12x+36[/tex]
Adding (-x² - 12x-36) on both sides
[tex]2x^2-12x+36-x^2-12x-36=x^2+12x+36-x^2-12x-36\\x^2-24x=0[/tex]
Taking x common;
[tex]x(x-24)=0\\[/tex]
Either,
x=0
or,
x-24 = 0 => x=24
As length cannot be 0 therefore,
Longer leg = x = 24 feet
Shorter leg = x-6 = 24-6 = 18 feet
Hypotenuse = x+6 = 24+6 = 30 feet.
The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.
Keywords: triangle, addition
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