question_answer

The sides of a triangle are 3 cm, 4 cm and 5 cm. The area (in \[\text{c}{{\text{m}}^{2}}\]) of the triangle formed by joining the mid-points of this triangle is

A) 6

B)  3

C)  \[\frac{3}{2}\]

D)  \[\frac{3}{4}\]

Correct Answer: C

Solution :

Given a = 3 cm, A = 4 cm, 0 = 5 cm

\[s=\frac{a+b+c}{2}=\frac{3+4+5}{2}\]

\[=\frac{12}{2}=6\]

From Hero's formula

Area of \[\Delta ABC=\sqrt{s\,\,(s-a)(s-b)(s-c)}\]

\[=\sqrt{6\,\,(6-3)(6-4)(6-5)}=6\,\,c{{m}^{2}}\]

Area of \[\Delta PQR=\frac{1}{4}\times \Delta ABC\]

\[=\frac{1}{4}\times 6=\frac{3}{2}\,\,\text{c}{{\text{m}}^{2}}\]