Year 11 Maths - Specialist Geometry in the plane and proof

Introduction to similarity

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Questions

Question 1

75487

In \(\Delta ABC:\,AB=12,\, \angle BAC=90^\circ\).

In \(\Delta DEC:\,ED=8,\,EC=15,\, \angle EDA=90^\circ,\,BE=x\). Find \(x\)

Answer

\(7.5\)

Worked Solution

\begin{align}
&\triangle ABC\ |||\ \triangle DEC \\
&\begin{aligned}\frac{BC}{AB}&=\frac{EC}{DE} \\
\frac{x+15}{12}&=\frac{15}{8} \\
x+15&=\frac{15 \times 12}{8} \\
x+15&=22.5 \\
\therefore\ x&=7.5
\end{aligned}\end{align}

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