Question

Two sides of a triangular field are 85m and 154m in length and its perimeter is 324m . find (1)the area of the field and (2) the length of the per pen dicular from the opposite vertex on the side measuring 154m

Answer 1

for the second one i think it is 115m

Answer 2

Given:

Perimeter of the triangular field (p) = 324m.

One side of the triangular field (a) = 85m.  

Another side of the triangular field (b) = 154m.

∴ The third side (c) = 324m – (154m + 85m) = 324m – 239m = 85m

Hence semi perimeter of the triangle(s) $=\frac{p}{2}=\frac{324}{2}\ m=162\ \mathrm{m}$

1. Using Heron’s Formula, $Area =\sqrt{s(s-a)(s-b)(s-c)}$

$\begin{array}{c}{=\sqrt{162(162-85)(162-154)(162-85)}\ m^{2}} \\ {=\sqrt{162 \times 77 \times 36 \times 77}\ m^{2}} \\ {=\sqrt{36} \times 77 \times 36 \times 77\ m^{2}} \\ {=36 \times 77\ m^{2}} \\ \bold{=2772\ m^{2}}\end{array}$

2. Let the length of the perpendicular from the opposite vertex on the side measuring 154m be x.

We know, $=\frac{1}{2} \times x \times 154\ m$

$\begin{array}{c}{\Rightarrow 2772\ m^{2}=\frac{1}{2} \times x \times 154\ m} \\ {\Rightarrow x=\frac{2772 \times 2 m^{2}}{154 m}=\frac{5544}{154}\ m=36 m}\end{array}$

Thus, the length of the perpendicular from the opposite vertex on the side measuring 154m is 36 m.