Question

find the missing side lengths. leave your answers as radicals in simplest form and round answers to the 100ths place 13) 14) 15) 16) 17) 18)

Explanation:

13)

• \(w=\frac{8}{3}\), \(y = \frac{8\sqrt{2}}{3}\approx3.77\), \(x=\frac{16}{3}\approx5.33\)

14)

• \(z=\frac{5\sqrt{7}}{2}\), \(y=\frac{5\sqrt{21}}{2}\approx11.46\), \(x = 5\sqrt{7}\approx13.23\)

15)

• \(y=\frac{\sqrt{30}}{2}\approx2.74\), \(x=\frac{\sqrt{15}}{2}\approx1.94\), \(w=\frac{\sqrt{30}}{2}\approx2.74\)

16)

• \(w = 2\), \(y = 2\sqrt{3}\approx3.46\), \(x = 4\sqrt{3}\approx6.93\)

17)

• \(w=\frac{\sqrt{21}}{3}\approx1.53\), \(y=\frac{\sqrt{7}}{3}\approx0.88\), \(x=\frac{\sqrt{42}}{3}\approx2.16\)

18)

• \(w = 5\sqrt{14}\approx18.71\), \(y = 5\sqrt{42}\approx32.40\), \(x = 10\sqrt{21}\approx45.83\)

Answer:

(13) \(w=\frac{8}{3},y = \frac{8\sqrt{2}}{3},x=\frac{16}{3}\)
(14) \(z=\frac{5\sqrt{7}}{2},y=\frac{5\sqrt{21}}{2},x = 5\sqrt{7}\)
(15) \(y=\frac{\sqrt{30}}{2},x=\frac{\sqrt{15}}{2},w=\frac{\sqrt{30}}{2}\)
(16) \(w = 2,y = 2\sqrt{3},x = 4\sqrt{3}\)
(17) \(w=\frac{\sqrt{21}}{3},y=\frac{\sqrt{7}}{3},x=\frac{\sqrt{42}}{3}\)
(18) \(w = 5\sqrt{14},y = 5\sqrt{42},x = 10\sqrt{21}\)