Question

The sides of a triangular field are 41m, 40m and 9m. Find the number
of rose beds that can be prepared in the field, if each rose bed on an
average needs 900 cm2
space.

Answer 1

Direct Answer:

2000 rose beds

Given:

A triangular field of sides 41m, 40m and 9m.

Proposed rose beds, each of area 900 cm².

To Find:

The no. of rose beds that can be prepared inside this field.

Solution:

At first, we need to find the area of the field which can be done by using the Heron's formula.

$\sf{\implies\:Heron's\:Formula:}$

$\sf{\sqrt{S(S-a)(S-b)(S-c)}}$

We know that:

Side, a = 41 m

Side, b = 40 m

Side, c = 9 m

So, semi-perimeter:

$\sf{=\dfrac{a+b+c}{2}}$

$\sf{=\dfrac{41+40+9}{2}}$

$\sf{=\dfrac{90}{2}}$

$\sf{=45\:cm}$

Now, applying the values we found into the formula:

$\sf{A=\sqrt{45(45-41)(45-40)(45-9)}}$

$\sf{A=\sqrt{45\times4\times5\times36}}$

$\sf{A=\sqrt{5\times9\times4\times5\times36}}$

All the values we have now are in the perfect square form and hence it is possible to take the square root of all of them.

$\sf{A=5\times3\times2\times6}$

$\sf{A=180\:m^2}$

Therefore, the area of the triangular field is 180 m².

In order to find the no. of rose beds, we need to divide the area of one bed from the total area. But, we can see that the units are different. So, we have to convert meters to centimeters by using the following conversion formula:

$\sf{\implies\:1m^2=10,000\:cm^2}$

In the same way,

$\sf{\implies\:180\:m^2=18,00,000\:cm^2}$

To find the no. of rose beds, required:

$\sf{\implies\:No.\:of\:rose\:beds=\dfrac{Area\:of\:field}{Area\:of\:one\:rose\:bed}}$

$\sf{\implies\:No.\:of\:rose\:beds=\dfrac{1800000}{900}}$

$\bf{\implies\:No.\:of\:rose\:beds=2000}$

Therefore, 2000 rose beds can be prepared in the triangular field.

Answer 2

Answer:

$\huge \tt \color{red}2000 \: rose \: beds$

Step-by-step explanation:

Area of triangular field=

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

$\bf \: S = \frac{a+b+c }{2} = \frac{41 +9+40}{2} = 45m$

::Area of triangular field=

$\bf \sqrt{45(45 - 41)(45 - 9)(45 - 40)}$

$\bf= 4 \times 5 \times 9= 180 {m}^{2}$

$\bf= 180 \times 1 {0}^{4} c {m}^{2}$

now, 900cm² area required for 1 rose bed 180 X 10⁴cm² area required for $\bf \frac{180 \times {10}^{4} }{900}$rose beds

$\bf \color{red}= > 2000 \: rose \: beds.$