How to find the legs of a right-angled triangle if the hypotenuse 6 and area 9 are known?

Let us express the length of the first unknown leg, for which we use the variable a.

Therefore, the length of the second unknown leg can be written in the form 9 * 2: a = 18 / a.

Since we know from the condition of the task that the hypotenuse is 6 conventional units, then we can write down the equation and find out the length of the legs:

a ^ 2 + 18 ^ 2 / a ^ 2 = 36;

a ^ 4 – 36a ^ 2 + 18 ^ 2 = 0;

(a ^ 2 – 18) ^ 2 = 0;

a ^ 2 – 18 = 0;

a ^ 2 = 18;

a1 = -√18 (not suitable);

a2 = √18;

18: √18 = √18.

Answer: Both legs will be equal to √18 conventional units.