Question

find the length of the missing side. (the triangle is not drawn to scale.)

1. a. 28 b. 100 c. 10 d. 48
2. a. 35 b. 49 c. 7 d. 2

find the length of the missing side. leave your answer in simplest radical form.

1. a. \\( \sqrt { 1 7 } \\) m b. 113 m c. \\( \sqrt { 1 1 3 } \\) m d. \\( \sqrt { 7 1 } \\) m
2. a. \\( \sqrt { 2 1 8 } \\) cm b. \\( 2 \sqrt { 5 } \\) cm c. \\( \sqrt { 6 } \\) cm d. \\( 2 \sqrt { 3 0 } \\)

Explanation:

Step1: Apply Pythagorean theorem for question 2

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let the missing side be \(a\), \(c = 25\), \(b=24\). Then \(a=\sqrt{c^{2}-b^{2}}=\sqrt{25^{2}-24^{2}}=\sqrt{(25 + 24)(25 - 24)}=\sqrt{49\times1}=7\)

Step2: Apply Pythagorean theorem for question 3

Let the missing side be \(c\), \(a = 7\), \(b = 8\). Then \(c=\sqrt{a^{2}+b^{2}}=\sqrt{7^{2}+8^{2}}=\sqrt{49 + 64}=\sqrt{113}\)

Step3: Apply Pythagorean theorem for question 4

Let the missing side be \(b\), \(a = 7\), \(c = 13\). Then \(b=\sqrt{c^{2}-a^{2}}=\sqrt{13^{2}-7^{2}}=\sqrt{(13 + 7)(13 - 7)}=\sqrt{20\times6}=\sqrt{120}=2\sqrt{30}\)

Answer:

1. \(d\)
2. \(c\)
3. \(c\)
4. \(d\)