The area of a right-angled triangle is 168cm2. Find its legs if the ratio of their lengths is 7/12.

We enter the proportionality coefficient k, then the legs of this right-angled triangle will be 7k and 12k.
We write down the formula for the area of a right-angled triangle with our data and solve the equation:
S = 1/2 * a * b.
1/2 * 7k * 12k = 168
84k = 336
k = 4
We find the legs:
7 * 4 = 28 (cm);
12 * 4 = 48 (cm).
Verification:
28/48 = 7/12.
Answer: the legs of the triangle are 7 cm and 12 cm.