Question

Use the formulas a = x 2 – y 2, b = 2xy, c = x 2 + y 2 to answer this question. One leg of a right triangle has length 11 and all sides are whole numbers. Find the lengths of the other two sides.
The other leg = ______ a0 and the hypotenuse =_______ a1

Answer 1

Let the legs of the right triangle be a and b and the hypothenus be c, then by the pythagoras theorem
$a^2+b^2=c^2$

Given that
$a =x^2-y^2$

Let a = 11, then
$x^2-y^2=11$

By trial and error, we can find that the value of x = 6 and the value of y = 5.
i.e.
$x^2-y^2=6^2-5^2=36-25=11$

Thus,
b = 2(6)(5) = 60
and
$x^2+y^2=6^2+5^2=36+25=61$

Therefore, the other leg = 60 and the hypotenuse = 61.