Question

Two sides of triangle are 85m and 154m in length and it's perimeter is 324m. Find (i)The area of the field and (ii) the length of the perpendicular from the opposite vertex on the side measuring 154m.

Answer 1

Given: Perimeter = 324m
Therefore X = 324 - 85 + 154
X = 85 m

(i) Area of field can be get by using Heron's Formula
Here, s = perimeter / 2
Therefore, s = 324/2 = 162 m

Area =
$\sqrt{s(s - a)(s - b)(s- c)}$
Therefore,
$\sqrt{162(162 - 85)(162 - 85)(162 - 154)}$
= 2772 m²

(ii) Now, length of the perpendicular from the opposite vertex on the side measuring 154m be y.
Now,
$area = (1 \div 2)(y)(154)$
Therefore, y = 36 m.