Question

Sides of a triangle are in the ratio of (8:7:3) and its perimeter is 180 cm, find its area?​

Answer 1

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Ratio of sides=8:7:3

Let the sides be x=8x:7x:3x

Given Perimter=180 cm

Perimeter of triangle= Sum of all sides

180=8x+7x+3x

$\large \tt \cancel\frac{180}{18} = x = 10$

Sides:-

8x=8×10=80 cm

7x=7×10=70 cm

3x=3×10=30 cm

Semi-Perimter=$\tt \frac{180}{2} = 90 \: cm$

Area of triangle=

$\sf \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \implies \sf \sqrt{90(90 - 80)(90 - 70)(90 - 30)} \\ \\ \sf \implies \sqrt{90 \times 40 \times 50 \times 60} \\ \\ \sf \implies \sqrt{9 \times 10 \times 4 \times 10 \times 5 \times 10 \times 6 \times 10} \\ \\ \sf \implies100 \sqrt{1080} \\ \\ \sf \implies100 \times 36.86 \\ \\ \sf \implies100 \times \frac{3686}{100} = 3686 {cm}^{2}$

${\underline{❥ʜᴏᴘᴇ \: ɪᴛ \: ʜᴇʟᴘs \: ʏᴏᴜ.....}}$

Answer 2

Answer:

Let side of the park be, a=5x,b=6x,c=7x

also, 2s=180m,

s=90m

now, a+b+c=180

5x+6x+7x=180

x=10

∴a=50m,b=60mbc=70m

Area of park=

90(90−50)(90−60)(90−70)

=

90×40×30×20

=

3×30×2×20×30×20

=20×30

6

=600

6

m

2