In figure, Triangle ABC is a right angled triangle at B. Given th… - Vidyadip

Question

In figure, Triangle ABC is a right angled triangle at B. Given that AB = 9cm, AC = 15cm and D, E are the mid-points of the sides AB and AC respectively, calculate

The length of BC
The area of $\triangle\text{ADE}.$

✓

Answer

I. In $\triangle\text{ABC},\angle\text{B}=90^\circ,$
By using Pythagoras theorem
AC² = AB² + BC²$\Rightarrow15^2=9^2+\text{BC}^2$
$\Rightarrow\text{BC}=\sqrt{15^2-9^2}$
$\Rightarrow\text{BC}=\sqrt{225-81}$
$\Rightarrow\text{BC}=\sqrt{144}=12\text{cm}$

II. In $\triangle\text{ABC},$
D and E are mid-points of AB and AC
$\therefore\text{DE}||\text{BC},=\frac{1}{2}\text{BC}$ [By mid−point theorem]
$\text{AD}=\text{DB}=\frac{\text{AB}}{2}=\frac{9}{2}=4.5\text{cm}$ $[\therefore$ D is the mid−point of AB$]$
Area of $\triangle\text{ADE}=\frac{1}{2}\times\text{AD}\times\text{DE}$
$=\frac{1}{2}\times4.5\times6$
$=13.5\text{cm}^2$

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