Question

27 find the missing side in the triangle below. round to tenths if necessary. 6.5 cm 10.2 cm x x = notes: look up the pythagorean theorem if you dont remember it.

Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 6.5\space\text{cm}\), \(b = 10.2\space\text{cm}\), and \(x\) is the hypotenuse.

Step2: Apply the Pythagorean theorem

Substitute the values of \(a\) and \(b\) into the formula. So \(x^{2}=(6.5)^{2}+(10.2)^{2}\). Calculate \((6.5)^{2}=6.5\times6.5 = 42.25\) and \((10.2)^{2}=10.2\times10.2=104.04\). Then \(x^{2}=42.25 + 104.04=146.29\).

Step3: Solve for \(x\)

Take the square root of both sides to find \(x\). \(x=\sqrt{146.29}\approx12.1\) (rounded to the tenths place).

Answer:

\(12.1\space\text{cm}\)