Question

the figure below shows a triangular wooden frame abc. the side ad of the frame has rotted and needs to be replaced
what is the length of the wood that is needed to replace ad?
6 2 inches
4 2 inches
6 0 inches
8 1 inches

Explanation:

Step1: Identify similar triangles

Triangles \(ABD\) and \(ACD\) are similar.

Step2: Set up proportion

Since \(\triangle ABD\sim\triangle ACD\), we have \(\frac{BD}{AD}=\frac{AD}{CD}\). Let \(AD = x\), \(BD = 4\), \(CD = 9\). Then \(\frac{4}{x}=\frac{x}{9}\).

Step3: Solve for \(x\)

Cross - multiply: \(x^{2}=4\times9 = 36\). Take square root: \(x = 6\) (length cannot be negative).

Answer:

6 inches