Question

triangular plot is given in the ratio 6:8:10 and its perimeter is 340 m.Find the area of the plot in m².​

Answer 1

Answer :-

• The area of the triangular plot is 11304.2998 m².

To find :-

• The area of the triangular plot.

Step-by-step explanation :-

• It is given that the three sides of the triangular plot are in the ratio 6 : 8 : 10.

Let :-

• The sides be 6x, 8x and 10x.

We know that :-

$\underline{ \boxed{ \sf Perimeter \: of \: a \: triangle = Sum \: of \: all \: sides}}$

Here,

• Perimeter = 340 m.

Therefore,

$\longrightarrow \tt 6x + 8x + 10x = 340$

$\longrightarrow \tt 24x = 340$

$\longrightarrow \tt{\cancel{\dfrac{340}{24}}}$

$\tt \longrightarrow x = 14.16$

Hence, the sides of the triangle are :-

$\bf 6x = 6 \times 14.16 = 84.96 \: m$

$\bf 8x = 8 \times 14.16 = 113.28 \: m$

$\bf 10x = 10 \times 14.16 = 141.6 \: m$

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• For finding the area of the triangular plot, first we need to find out it's semi perimeter.

We know that :-

$\underline{\boxed{\sf{Semi-perimeter = \dfrac{Sum \: of \: three \: sides}{2}}}}$

Here,

• The sides are 84.96 m, 113.28 m and 141.6 m.

Therefore,

$\sf{Semi-perimeter = \dfrac{84.96 + 113.28 + 141.6}{2}}$

$\sf{ Semi-perimeter = \dfrac{84.96 + 113.28 + 141.6}{2}}$

$\sf{ Semi-perimeter = \cancel{ \dfrac{340}{2}}}$

$\sf{Semi-perimeter = 170 \: m}$

Now, we know that :-

$\underline{\boxed{\sf{Area \: of \:a \: triangle = \sqrt{s(s - a) (s - b) (s - c}}}}$

Here,

• Semi-perimeter = 170 m.
• The sides are 84.96 m, 113.28 m and 141.6 m.

Therefore,

$\sf{ Area = \sqrt{s(s - a) (s - b) (s - c)}}$

$\sf{ Area = \sqrt{170(170 - 84.96) (170 - 113.28) (170 - 141.16)}}$

$\sf{ Area = \sqrt{170(155.84)(85.04)(56.72)}}$

$\sf Area = \sqrt{127787194.22}$

$\sf Area = 11304.2998 \: m^2$

Hence,

• The area of the triangular plot is 127787194.22 m².

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