To find the length of the other leg in a right triangle where the hypotenuse and one leg are known, we can use the Pythagorean theorem. The Pythagorean theorem states that for a right triangle:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
where [tex]\( c \)[/tex] is the length of the hypotenuse and [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the lengths of the other two legs.
In this problem:
- The hypotenuse [tex]\( c = 25 \)[/tex] cm.
- The shorter leg [tex]\( a = 15 \)[/tex] cm.
We need to find the length of the other leg [tex]\( b \)[/tex].
We start by plugging the known values into the Pythagorean theorem:
[tex]\[ 15^2 + b^2 = 25^2 \][/tex]
Next, we square the known values:
[tex]\[ 225 + b^2 = 625 \][/tex]
To isolate [tex]\( b^2 \)[/tex], subtract 225 from both sides of the equation:
[tex]\[ b^2 = 625 - 225 \][/tex]
[tex]\[ b^2 = 400 \][/tex]
Finally, to find [tex]\( b \)[/tex], we take the square root of both sides:
[tex]\[ b = \sqrt{400} \][/tex]
[tex]\[ b = 20 \][/tex]
Therefore, the length of the other leg of the right triangle is [tex]\( 20 \)[/tex] cm.
