The sum of the legs of a right-angled triangle is 7 cm, the area of the triangle is 6 cm square. Find the hypotenuse.

Let the first leg be equal to the variable a.

Then, in accordance with the conditions of our problem, the second leg can be represented in the form of 7 – a.

Since we know from the condition that the area of the triangle is 6 cm2, then we are able to write down the equation and determine the lengths of the legs:

a * (7 – a): 2 = 6;

a ^ 2 – 7a + 12 = 0;

D = 49 – 48 = 1;

a1 = (7 – 1): 2 = 3;

a2 = (7 + 1): 2 = 4.

Let’s find out what the length of the hypotenuse will be equal to with such legs:

√ (3 ^ 2 + 4 ^ 2) = √25 = 5.

Answer: 5 centimeters.