97cm, a, 72cm

What is the length of the missing leg? If necessary, round to the nearest tenth.
a=__ centimeters

1 answer

To find the length of the missing leg, we need more context regarding the shape of the triangle or the values provided. However, it looks like you might be referring to a right triangle where:

  • One leg is 72 cm.
  • The other leg is 'a' cm.
  • The hypotenuse is 97 cm.

If that's the case, we can use the Pythagorean theorem, which states:

\[ a^2 + b^2 = c^2 \]

where:

  • \(c\) is the hypotenuse,
  • \(a\) and \(b\) are the two legs.

In this scenario:

  • \(c = 97\) cm (hypotenuse)
  • \(b = 72\) cm (one leg)
  • \(a = ?\) (the missing leg)

Now we can rearrange the formula to solve for \(a\): \[ a^2 + 72^2 = 97^2 \]

Calculating the squares: \[ a^2 + 5184 = 9409 \]

Now, subtract 5184 from both sides: \[ a^2 = 9409 - 5184 \] \[ a^2 = 4225 \]

Now take the square root of both sides: \[ a = \sqrt{4225} = 65 \]

Thus, the length of the missing leg \(a\) is: \[ a = 65 \text{ centimeters} \]