The area of a right-angled triangle is 12 cm2 and one of the legs is 2 cm larger than the other

The area of a right-angled triangle is 12 cm2 and one of the legs is 2 cm larger than the other. Find the length of the smaller leg.

Let us express the length more than the leg, for which we take the variable a.

Then the length of the smaller leg can be expressed through (a – 2).

Therefore, the area of our triangle can be expressed as 1/2 * a * (a – 2).

Since we know that the area of a triangle is 12 square centimeters, then we write down the equation and find out the length of the smaller leg:

1/2 * a * (a – 2) = 12;

a ^ 2 – 2a – 24 = 0;

D = 4 + 4 * 24 = 100 = 102;

a1 = (2 + 10): 2 = 6;

a2 = (2 – 10): 2 = -4 (not suitable);

6 – 2 = 4.

Answer: 4 cm.