Question

For a triangle whose sides are 50 m, 78 m and 112 m, respectively, then the length of the perpendicular from the opposite angle on the side 112 m is _____.

• A. 45 m
• B. 35 m
• C. 30 m
• D. 95 m
• E. None of these

Answer 1

The correct option is C 30 m

We have, $2s=50+78+112=240$
$\therefore s=120.$
$\therefore Area=\sqrt{120(120-50)(120-78)(120-112)}$
$=\sqrt{120\times 70\times 42\times 8}=\sqrt{2^3\times 5\times 3\times 7\times 5\times 2\times 2\times 7\times 3\times 2^2}=2^4\times 5\times 3\times 7=1680m^2\therefore \frac{1}{2}\times 112\times h=1680,$
where h is the length of the perpendicular
$\therefore h=\frac{1680\times 2}{112}=30m$