The area of a right-angled triangle is 24 cm2. if one leg is reduced by one cm and the other

The area of a right-angled triangle is 24 cm2. if one leg is reduced by one cm and the other is increased by 3, then the area will be 27.5 cm2, find the lengths of the legs of the triangle, solve it as an equation.

Let the legs of the original right-angled triangle be a cm and b cm.Then the legs of the derived right-angled triangle, in accordance with the condition of the task, will be (a – 1) cm and (b + 3) cm, respectively. Based on all these data, we compose and solve the system equations:

(a * b) / 2 = 24;
((a – 1) * (b + 3)) / 2 = 27.5.

a * b = 48;
(a – 1) * (b + 3) = 55.

a = 48 / b;
(48 / b – 1) * (b + 3) = 55.

b ^ 2 + 10 * b – 144 = 0;

b1 = 8;
b2 = – 18 (not beats conv.).

Then a = 48/8 = 6 (cm).

Answer: 6 cm and 8 cm.