Given the information about the right triangle we have the following:
since we have that the longer leg is 7cm more than the shorter leg, then:

and also the hypotenuse is 14 cm more than the shorter leg, therefore:

with these two expressions, we can find the value of the shorter leg:

we have then that a=21 or a=-7. We choose a=21 since distances cannot be negative. Now we can find the value of b and c and check if they match using the pythagorean theorem again:
![\begin{gathered} a=21 \\ b=a+7=21+7=28 \\ c=a+14=21+14=32 \\ c^2=a^2+b^2 \\ \Rightarrow c^2=21^2+28^2=1225 \\ \Rightarrow c=\sqrt[]{1225}=35 \\ c=35 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/llv57dxlybvlc97cfx4um70mquo67n591w.png)
therefore, the sides of the triangle should be 21 cm, 28 cm and 35 cm long