

View Answer
Shortcut:
If a, b and c are the lengths of the sides of a triangle and
S =
1
/
2
(a + b + c), then
Area of triangle = √[s(s − a)(s − b)(s − c)]
Here, a = 50, b = 78, c = 112,
s =
1
/
2
(50 + 78 + 112) = 120
Using these values in the shortcut, we get:
Area = √[120(120 − 50)(120 − 78)(120 − 112)]
= √(120 x 70 x 42 x 8) = 1680
Hence, area of triangle is 1680 sq metre.
Perpendicular = 2 x
Area
/
Base
=
1680 x 2
/
112
= 30
Hence, the perpendicular is 30 m

