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Find the length of the other leg of a right triangle with a hypotenuse of [tex][tex]$25 \, \text{cm}$[/tex][/tex] and a shorter leg of [tex][tex]$15 \, \text{cm}$[/tex][/tex].

Sagot :

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.