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From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.

From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.-example-1
User Korbbit
by
7.2k points

1 Answer

3 votes

Given:

• AD = 3

,

• DC = 27

,

• BD = x + 3

Let's solve for x.

To solve for x, apply the altitude formula:


(AD)/(BD)=(BD)/(DC)

Where BD is the altitude.

Cross multiply:


BD^2=AD*DC

Plug in the values and solve for x:


\begin{gathered} (x+3)^2=3*27 \\ \\ (x+3)^2=81 \end{gathered}

Take the square root of both sides:


\begin{gathered} √((x+3)^2)=√(81) \\ \\ x+3=9 \\ \\ \text{ Subtract 3 from both sides:} \\ x+3-3=9-3 \\ \\ x=6 \end{gathered}

Therefore, the value of x is 6 .

ANSWER:

d. 6

User Kaminari
by
5.8k points
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