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What is the value of a?

 

 Mar 22, 2021
 #1
avatar+544 
+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
avatar+1425 
+6

3 / 4 = 4 / a 

 

a = 16 / 3

 

a = 5 1/3

 Mar 22, 2021
edited by Guest  Mar 22, 2021

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