Question

In the accompanying diagram of right trianglesABD and DBC, AB = 5, AD = 4, and CD=1. Findthe length of BC, to the nearest tenth.B5AYour answer

Answer 1

Given:

AB = 5

AD = 4

CD = 1

Let's find the length of BC.

To find the length of BC, apply the Angle Bisector Theorem of similar triangles.

We have the equation:

$\frac{AB}{AD}=\frac{BC}{CD}$

Input values into the equation:

$\frac{5}{4}=\frac{BC}{1}$

Cross multiply to find BC:

$\begin{gathered} 4(BC)\text{ = 5(1)} \\ \\ 4(BC)=5 \\ \\ \text{Divide both sides by 4:} \\ \frac{4(BC)}{4}=\frac{5}{4} \\ \\ BC=1.25\approx1.3 \end{gathered}$

Therefore, the length of BC to the nearest tenth is 1.3

ANSWER:

1.3