Question

How do I solve the length of AC?​

Answer 1

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∆ABC and ∆ADE are similar triangles.

Thus ;

`(AD)/(AC) = (DE)/(BC) = (AE)/(AB) \\`

So :

`(5)/(3 + 2x) = (4)/(8) \\`

`(5)/(3 + 2x) = (1)/(2) \\`

Inverse both sides

`(3 + 2x)/(5) = (2)/(1) \\`

`(2x + 3)/(5) = 2 \\`

Multiply sides by 5

`5 * (2x + 3)/(5) = 5 * 2 \\`

`2x + 3 = 10`

Thus ;

`AC = 2x + 3 = 10`

`AC = 10`

Done...

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