The length of the hypotenuse of a right-angled triangle is 37 cm and its area is 210 cm2, find the length of the legs.

1. The area of ​​a right-angled triangle is equal to the product of the legs divided by 2.

According to the condition of the problem, it is 210 cm2.

Then the product of the legs is 210 * 2 = 420 cm2.

2. Let X cm be the length of one leg.

Then 420 / X cm is the length of the second.

It is known that the hypotenuse is 37 cm.

Using the Pythagorean theorem, we write down the correspondence between the sides of the triangle.

X * X + 420 / X * 420 / X = 37 * 37.

Denote Y = X * X.

We make a substitution and bring it to a common denominator.

Y * Y – 1369 * Y + 420 * 420 = 0.

Discriminant D = 1369 * 1369 – 420 * 420 * 4 = 1168561

Y1 = (1369 – 1081) / 2 = 144, then X = 12, second leg 420/12 = 35.

Y2 = (1369 + 1081) / 2 = 1225, then X = 35, the second leg is 420/35 = 12.

Answer: The lengths of the legs are 12 cm and 35 cm.