Question

97cm, a, 72cm
What is the length of the missing leg? If necessary, round to the nearest tenth.
a=__ centimeters

Answer 1

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:
\[
a = 65 \text{ centimeters}
\]