The area of a right-angled triangle is 726 cm2, the hypotenuse is 55 cm. Find the smaller leg.

Let the legs be equal to x and y, the hypotenuse – c.

The area of a given right-angled triangle is found as follows: x * y / 2 = 726.

Also, by the Pythagorean theorem, c ^ 2 = x ^ 2 + y ^ 2.

From the first formula we express x: x = 726 * 2 / y = 1452 / y. Substitute in the second formula: 55 ^ 2 = (1452 / y) ^ 2 + y ^ 2

3025 = 2108304 / y ^ 2 + y ^ 2

3025 = (2108304 + y ^ 4) / y ^ 2

We get the equation y ^ 4 – 3025 * y ^ 2 + 2108304 = 0. Let y ^ 2 = t.

t ^ 2 – 3025 * t + 2108304 = 0,

t1 = 1089 = y ^ 2 => y = 33,

t2 = 1936 = y ^ 2 => y = 44.

In response, write down the smaller root, that is, 33.