Question

In the diagram below of angle ADB, m angle BDA = 90,AD=5 2, and AB = 2 5.What is the length of BD

Answer 1

The triangle BDA is a right-angled triangle where $\begin{gathered} To find the length of BD, Pythagorean theorem can be used to determine the unknown side,

[tex]\begin{gathered} \text{Pythagorean theorem,} \\ (\text{Hypotenuse)}^2=(\text{Opposite)}^2+(\text{Adjacent)}^2 \end{gathered}$$\begin{gathered} \text{Where AB is the hypotenuse} \\ BD\text{ is the opposite and} \\ AD\text{ is the adjacent} \end{gathered}$

Substituting for AB and AD into the theorem to find unknown BD,

$\begin{gathered} (AB)^2=(BD)^2+(AD)^2 \\ (2\sqrt[]{15})^2=(BD)^2+(5\sqrt[]{2})^2 \\ 60=(BD)^2+50 \\ (BD)^2=60-50 \\ (BD)^2=10 \\ \text{square roots of both sides} \\ \sqrt[]{(BD)}^2=\sqrt[]{10} \\ BD=\sqrt[]{10} \end{gathered}$

Hence, length of BD is sqrt 10.