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# Right Triangle Similarity

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50
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What is the value of a?

Mar 22, 2021

#1
+492
+2

c = $$\sqrt{3^2 + 4^2} = 5$$

This means b = $$\sqrt{(a + 3)^2 - c^2}$$

but b also equals = $$\sqrt{a^2 + 4^2}$$

We can put these two into an equation:

$$\sqrt{(a + 3)^2 - c^2} = \sqrt{a^2 + 4^2}$$

$$a^2 + 6a + 9 - c^2 = a^2 + 16$$

$$6a - c^2 = 7$$

and since c = 5,

$$6a - 25 = 7$$

$$6a = 32$$

$$a = 5\frac{1}{3}$$

Mar 22, 2021
#2
+1164
+6

3 / 4 = 4 / a

a = 16 / 3

a = 5 1/3

Mar 22, 2021
edited by Guest  Mar 22, 2021