Question

Q.5) The perimeter of a triangular plot is 180 m. It's sides are in a fixed ratio 5:6:7 .Find the total area of triangular plot.

Answer 1

GIVEN :

• The perimeter of a triangular plot is 180 m. It's sides are in a fixed ratio 5:6:7 .

TO FIND :

• The total area of triangular plot = ?

SOLUTION :

Let the 3 sides of a triangle be 5x + 6x + 7x = 18x

Perimeter = 180 m .....(given)

Perimeter = a + b + c

180 = 18x

x = 10 m

Here,

a = 5x = 5 × 10 = 50

b = 6x = 6 × 10 = 60

c = 7x = 7 × 10 = 70

Semi Perimeter = a + b + c/2

Semi Perimeter = 50 + 60 + 70/2

Semi Perimeter = 180/2

Semi Perimeter = 90 m

★ By using herons formula :

$\large{\boxed{\bf \sqrt{s(s - a)\: (s - b)\: (s - c)}}}$ ★

➨$\sf \sqrt{90(90 - 50)\: (90 - 60)\: (90 - 70)}$

➨$\sf 300 \times 2\sqrt{6}$

➨$\pink{\sf 600 \sqrt{6}\:m^2}$

Therefore, the total area of triangular plot is 600√6 m².

Answer 2

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▶QUESTION :

➠ The perimeter of a triangular plot is 180 m. It's sides are in a fixed ratio 5:6:7 .Find the total area of triangular plot .

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▶ANSWER :

☯ GIVEN -

➡ Perimeter of triangular plot = 180 m

➡ Ratio of sides = 5:6:7

☯ TO FIND -

➡ Total area of triangular plot

☯ SOLUTION -

⏹ Let the side be x . Then ,

➡ 5x + 6x + 7x = 180

➡ 18x = 180

➡ x = $\dfrac{180}{8}$

➡ x = 10 m

SIDES -

a = 5x = 5(10)=50m,

b=6x=6(10)=60m,

c=7x=7(10)=70m.

⏹ Now , let us find area by HERON'S FORMULA that is -

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

⚡ Here , s is semi-perimeter and a, b, c are the sides of traingle .

➡ Given perimeter = 180 m

➡ Semi-perimeter = $\dfrac{a+b+c}{2}$

➡ Semi-perimeter = $\dfrac{180}2$ = 90 m

⏹ Now , a=50, b=60, c=70

$area = \sqrt{90(90- 50)(90 - 60)(90 - 70)}$

$area = \sqrt{90 \times 40 \times 30 \times 20}$

$area = \sqrt{10000 \times 9 \times 4 \times 3 \times 2}$

$area = 100 \times 3 \times 2 \sqrt{3 \times 2}$

$area = 600 \sqrt{6} \: {m}^{2}$

⚡AREA = 600√6 m^2

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