Question

If the extremities of the base of an isosceles triangle are the points $(2a,0)$ and $(0,a)$ and the equation of one of the sides is $x=2a,$ then the area of the triangle, in square units, is :

• A. $\frac{1}{5}{a}^2$
• B. $\frac{5}{2}{a}^2$
• C. $\frac{25a^2}{4}$
• D. $5a^2$

Answer 1

The correct option is A $\frac{1}{5}{a}^2$

$\begin{array}{c}{\left(2a\right)}^2+{\left(y-4\right)}^2=y^2\\ y=\frac{5}{2a}\\ DE=\left(9,\frac{9}{2}\right)\\ AD=\sqrt{5}a\\ BC=\sqrt{5}a\\ area=\frac{1}{5}{a}^2\end{array}$