The area of a right-angled triangle is 84 cm², and the difference in the length of the legs is 17 cm. Find the legs.

The area of a right-angled triangle is equal to half the product of its legs (sides forming a right angle). Let’s solve the problem using the equation:

Let x be the smaller leg;

Then: (x + 17) cm – larger leg;

Let’s compose the equation for the area of the triangle and find x:

x * (x + 17) * 1/2 = 84 cm²;

(x² + 17x) * 1/2 = 84 cm²;

0.5x² + 8.5x = 84;

0.5x² + 8.5x – 84 = 0;

x = 7 cm – smaller leg;

(x + 17) = 7 + 17 = 34 cm – larger leg.

Answer: 7 cm, 34 cm