To better understand the statement, it is convenient to first draw a drawing:
The formula to find the area of a triangle is
As you can see in this case you have the measurement of the area and the base, so you can get the measurement of its height:
![\begin{gathered} A=120\operatorname{cm} \\ 120\operatorname{cm}=(24cm\cdot h)/(2) \\ \text{ Multiply by 2 from both sides of the equation} \\ 120\operatorname{cm}\cdot2=(24cm\cdot h)/(2)\cdot2 \\ 240\operatorname{cm}=24cm\cdot h \\ \text{ Divide by 24 cm from both sides of the equation} \\ \frac{240\operatorname{cm}}{24\operatorname{cm}}=\frac{24cm\cdot h}{24\operatorname{cm}} \\ 10\operatorname{cm}=h \end{gathered}]()
Now, since it is a right triangle then you can use the Pythagorean Theorem formula to find the length of the hypotenuse:
Graphically,
So, you have
![\begin{gathered} a=24\operatorname{cm} \\ b=10\operatorname{cm} \\ c=\text{ ?} \\ a^2+b^2=c^2 \\ (24cm)^2+(10cm)^2=c^2 \\ 576cm^2+100cm^2=c^2 \\ 676cm^2=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{676\operatorname{cm}^2}=\sqrt[]{c^2} \\ 26\operatorname{cm}=c \end{gathered}]()
Therefore, the length of the hypotenuse of the right triangle is 26 centimeters.