Question

If the area of the triangle whose side lengths are a, b and c is x .Then the area of triangle formed by joining the midpoints of the sides of the triangle is

• A. $\frac{x}{2}$
• B. $x$
• C. $\frac{x}{4}$
• D. $\frac{x}{8}$

Answer 1

The correct option is C $\frac{x}{4}$

If the side lengths of the triangle area, b and c.
Semi perimeter $s=\frac{(a+b+c)}{2}$
Area of the triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
The sides of the triangle formed by joining the points are $\left(\frac{a}{2}\right)$,$\left(\frac{b}{2}\right)$ and $\left(\frac{c}{2}\right)$
Semi perimeter = $\frac{(a+b+c)}{4}$
= $\left(\frac{s}{2}\right)$
Area of the triangle = $\frac{1}{4}\sqrt{s(s-a)(s-b)(s-c)}$
= $\left(\frac{X}{4}\right)$