Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

1. First, identify the type of triangle and the relevant formula:

• Since the triangle has a right - angle (indicated by the small square in the corner), we can use the Pythagorean theorem, which is \(a^{2}+b^{2}=c^{2}\) for a right - triangle, where \(c\) is the hypotenuse (the longest side) and \(a\) and \(b\) are the other two sides.
• Here, the two given sides are \(a = 24\) and \(c = 26\). We need to find the other side \(b\).
• Rearranging the Pythagorean theorem to solve for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).

1. Then, substitute the values into the formula:

• Substitute \(a = 24\) and \(c = 26\) into the formula \(b=\sqrt{c^{2}-a^{2}}\).
• First, calculate \(c^{2}-a^{2}\): \(26^{2}-24^{2}=(26 + 24)(26 - 24)\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)).
• \((26 + 24)(26 - 24)=(50)\times(2)=100\).
• Then, \(b=\sqrt{100}=10\).

Answer:

10