Question

△bcd ~ △pqr. find bc.
d
3
b
5
c
q
45
p
27
r
bc = \square

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle BCD\sim\triangle PQR\), the ratios of corresponding sides are equal. That is \(\frac{BC}{PQ}=\frac{BD}{PR}\).

Step2: Substitute the known values

We know \(BD = 3\), \(PR=27\), and \(PQ = 45\). Let \(BC=x\). Then \(\frac{x}{45}=\frac{3}{27}\).

Step3: Solve the proportion

Cross - multiply: \(27x=3\times45\). So \(27x = 135\). Divide both sides by 27: \(x=\frac{135}{27}=5\).

Answer:

\(5\)