The sides of a right triangle are in the ratio 7:24:25. If the hypotenuse is 50 cm, what is the shorter leg?

To find the length of the shorter leg of the right triangle when the sides are in the ratio of 7:24:25 and the hypotenuse is 50 cm, you start by understanding the relationship among the sides as given by their ratio.

In a right triangle, the sides can be expressed using a variable, often denoting the shortest leg as 7x, the other leg as 24x, and the hypotenuse as 25x, where x is a common multiplier. For this triangle, we know the hypotenuse is 50 cm, which corresponds to 25x.

To find x, you can set up the equation:

[ 25x = 50 ]

Solving for x gives:

[ x = \frac{50}{25} = 2 ]

Now that you have x, you can find the lengths of the legs:

• The shorter leg is 7x, which is:

[ 7x = 7 \cdot 2 = 14 \text{ cm} ]

Thus, the length of the shorter leg is indeed 14 cm. This aligns with the ratio provided, confirming that the calculations are correct and the relationships inherent to a right triangle