Question

① find the length o
a.
7cm
9 cm

Explanation:

Step1: Identify the triangle type

This is a right - triangle with legs \(a = 9\space cm\) and \(b=7\space cm\). We can use the Pythagorean theorem, which states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 9\) and \(b = 7\) into the formula:
\(c^{2}=9^{2}+7^{2}\)
\(c^{2}=81 + 49\)
\(c^{2}=130\)

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{130}\approx11.4\space cm\) (if we want a decimal approximation) or we can leave it as \(\sqrt{130}\space cm\).

Answer:

The length of the hypotenuse is \(\sqrt{130}\space cm\approx11.4\space cm\)