Question

24 multiple choice 2 points a triangle has sides whose lengths are 5, 12, and 13. a similar triangle could have sides with lengths of 10, 24, and 26 6, 8, and 10 3, 4, and 5 7, 24, and 25 25 multiple choice 2 points find x. 2√3 15 9 12

Explanation:

Step1: Recall the property of similar triangles

For similar triangles, the ratios of corresponding side lengths are equal.

Step2: Check the first option

For the triangle with sides \(5,12,13\) and the triangle with sides \(10,24,26\), \(\frac{10}{5} = 2\), \(\frac{24}{12}=2\), \(\frac{26}{13}=2\). The ratios are equal.

Step3: Check the second option

For the triangle with sides \(5,12,13\) and the triangle with sides \(6,8,10\), \(\frac{6}{5}=1.2\), \(\frac{8}{12}=\frac{2}{3}\approx0.67\), the ratios are not equal.

Step4: Check the third option

For the triangle with sides \(5,12,13\) and the triangle with sides \(3,4,5\), \(\frac{3}{5} = 0.6\), \(\frac{4}{12}=\frac{1}{3}\approx0.33\), the ratios are not equal.

Step5: Check the fourth option

For the triangle with sides \(5,12,13\) and the triangle with sides \(7,24,25\), \(\frac{7}{5}=1.4\), \(\frac{24}{12} = 2\), the ratios are not equal.

Step6: Recall the property of tangent to a circle

If \(PA\) and \(PB\) are tangents to a circle from an external point \(P\), then \(PA=PB\). Here \(PA = 12\), so \(x=12\).

Answer:

1. \(10,24,\text{and }26\)
2. \(12\)