Question

Two sides of a triangular field are 85 m and 154 m in length and its perimeter is 324 m.
Find (i) the area of the field and (ii) the length of the perpendicular from the opposite vertex on the side measuring 154 m.
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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

We are given that two sides of triangular field are 85 M and 154 m

Perimeter of triangle = 324 M

Let the third side be x

Perimeter of triangle =Sum of all sides

$\Rightarrow85+154+x </p><p>$

$\Rightarrow239+x$

Since we are given that Perimeter of triangle = 324M;

$So, \Rightarrow 324 = 239 +x;</p><p>$

$\Rightarrow324 - 239 = x; \\ </p><p> </p><p> \Rightarrow8 5 = x \\ </p><p>$

Now we will use heron's formula to find the area of triangle

$\rightarrow \: a = 85m \\ </p><p> \rightarrow \: b = 154m; \\ </p><p> \rightarrow \: c = 85m; \\ </p><p> </p><p>Area = \sqrt{(s(s - a) \times (s - b) \times (s - c))} ; \\ \\ s \rightarrow\frac{ (a + b + c)}{2}$

Substitute the values:

$\rightarrow \: s = \frac{(85 + 154 + 85)}{2} \\ \\ \\ \\ </p><p></p><p></p><p>\Rightarrow s = 162; \\ \\ \\ \\ </p><p> </p><p>\Rightarrow \: Area =; \sqrt{162(162-85)(162-154)(162-85)} ;</p><p>$

${\boxed{ \green {\Rightarrow \: Area = 2772}}}$

So, Area of triangle is 2772

Now rto find the length of the perpendicular from the opposite vertex on the site measuring 154 m

$Area = \frac{1}{2} \times B a s e \times H e i g h t;$

2772 = 1/2 ×154 ×H e i g h t;

(2772 ×2)/154 = Height;

36 = Height

Hence Area of triangle is 2772 and he length of the perpendicular from the opposite vertex on the site measuring 154 m is 36 m