Question

The sides of a triangular field are 7 m , 15m and 20 m . find the number of rose beds that can be prepared in the field , if each , rose bed, on an average needs 200 cm ^2 space.​

Answer 1

Answer:

There can be 2100 rosebeds in the triangular field.

Step-by-step explanation:

Sides of triangle = 7 m, 15 m and 20 m

A rose bed needs area of = 200 cm² = 0.02 m²

_______________________

Find the area of triangle. Using the Heron's Formula,

$\bigstar\:{\boxed{\sf{Semi \: Perimeter = \dfrac{a + b + c}{2}}}}$

• a = 7 m
• b = 15 m
• c = 20 m

$\sf{\longrightarrow{Semi \: Perimeter = \dfrac{7 + 15 + 20}{2}}}$

$\sf{\longrightarrow{Semi \: Perimeter = \dfrac{42}{2}}}$

$\sf{\longrightarrow{Semi \: Perimeter =21 \: m}}$

Semi Perimeter is 21 m.

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Heron's Formula,

$\bigstar \: \boxed{\sf{ \sqrt{s(s - a)(s - b)(s - c)} }}$

• s = 21 m
• a = 7 m
• b = 15 m
• c = 20 m

$\sf{\longrightarrow} \: \sqrt{21(21 - 7)(21- 15)(21- 20)}$

$\sf{\longrightarrow} \: \sqrt{21 \times 14 \times 6 \times 1}$

$\sf{\longrightarrow} \: \sqrt{7 \times 3 \times 7 \times 2 \times 2 \times 3 \times 1}$

$\sf{\longrightarrow} \: 7 \times 3 \times 2 \times 1$

$\sf{\longrightarrow} \: 42 \: {m}^{2}$

Area of triangle = 42 m²

_______________________

Number of rose beds =

$\bigstar\:{\boxed{\sf{No. \: of \: Rose \: beds = \dfrac{Area \: of \: triangle}{Area \: of \: rose \: bed}}}}$

• Area of triangle = 42 m²
• Area of a rose bed = 0.02 m²

$\sf{\longrightarrow} \: \dfrac{42}{0.02}$

$\sf{\longrightarrow} \: \dfrac{4200}{2}$

$\sf{\longrightarrow} \: 2100$

Number of rose beds = 2100

Therefore, there can be 2100 rosebeds in the triangular field.

Answer 2

Answer:

Given :-

The side of a triangular field are 7 m , 15m and 20 m .

To Find :-

Number of rose bed can be prepared

Solution :-

According to the question

Area of triangle = a + b + c/2

Semiperimeter = 7 + 15 + 20/2

Semiperimeter = 42/2

Semiperimeter = 21 m

Now

Area = √s(s - a)(s - b)(s - c)

Area = √21(21 - 7)(21 - 15)(21 - 20)

Area = √21 × 14 × 6 × 1

Area = √1764

Area = 42 m²

Now

1 m² = 10,000 cm²

No. of rose bed may made = 42/200/10,000

No. of rose bed may made = 42/200 × 10000

No. of rose bed may made = 2100