Find the hypotenuse of a right-angled triangle whose area is 96 cm2, and the legs are 3: 4.

If the legs of a right-angled triangle are 3: 4, then this means that one leg contains 3 parts of the length, and the second leg – 4 of the same length.

Let the length of one part be x cm, then the first leg is 3x cm, and the second leg is 4x cm.The area of ​​a right triangle is half the product of its legs, i.e. 1/2 * 3x * 4x cm ^ 2 or 96 cm ^ 2. Let’s make an equation and solve it.

1/2 * 3x * 4x = 96;

6x ^ 2 = 96;

x ^ 2 = 96: 6;

x ^ 2 = 16;

x = 4 (cm) – the length of one part;

3x = 4 * 3 = 12 (cm) – the length of the first leg;

4x = 4 * 4 = 16 (cm) – the length of the second leg.

Let’s find the hypotenuse of a triangle by the Pythagorean theorem: The square of the hypotenuse is equal to the sum of the squares of the legs: c ^ 2 = a ^ 2 + b ^ 2;

c ^ 2 = 12 ^ 2 + 16 ^ 2;

c ^ 2 = 144 + 256;

c ^ 2 = 400;

s = 20 (cm).

Answer. 20 cm.