Question

The sides of a triangular field are 225m, 375m, 300m. Each rose bed requires 750cm² of area. How many rose beds can be prepared in the field?​

Answer 1

$\\ \large{ \underline{ \underline{ \sf{ \pmb{Question}}}}}$

The sides of a triangular field are 225m, 375m, 300m. Each rose bed requires 750cm² of area. How many rose beds can be prepared in the field?

$\\ \large{ \underline{ \underline{ \sf{ \pmb{Required \: Answer}}}}}$

$\\ \underline{ \underline{ \sf{ \frak{Given}}}}$

• Sides of a triangle field are 225m, 375m, 300m.
• Each rose bed's area is 750cm²

$\\ \underline{ \underline{ \sf{ \frak{To \: Find}}}}$

• Number of rose beds can be prepared in the field.

$\\ \underline{ \underline{ \sf{ \frak{Solution}}}}$

Let,

• 1st side of the triangle be a = 225m
• 2nd side of the triangle be b = 375m
• 3rd side of the triangle be c = 300m
• Semi-perimeter of the triangle be s

We know that,

$\\ \underline{ \boxed{ \tt{ \color{navy}{s = \dfrac{a + b + c}{2} }}}}$

Therefore,

$\sf{\bold{s = \dfrac{225 + 375 + 300}{2} m}}$

$\\ \sf{ \implies{ \bold{s} = \dfrac{900}{2} }}m$

$\\ \therefore{ \sf{ \bold{s = 450m}}}$

Again, from Heron's formula, we know that:-

$\\ \underline{ \boxed{ \tt{ \color{navy}{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} square \: units}}}}$

We have,

• a = 225m
• b = 375m
• c = 300m
• s = 450m

Substituting the values:-

$\\ \sf{ \bold{Area \: of \: the \: triangle \: field = \sqrt{450(450 - 225)(450 - 375)(450 - 300)} squre \: meters}}$

$\\ \sf{ \implies{Area \: of \: the \: triangle \: field = \sqrt{450 \times 225 \times 75 \times 150} \: squre \: meters}}$

$\\ \sf{ \implies{Area \: of \: the \: triangle \: field = \sqrt{1139062500} \: squre \: meters}}$

$\\ \sf{ \therefore{Area \: of \: the \: triangle \: field = \bold{33750 \: square \: meters}}}$

Again, we were given,

• Area of each road bed = 750cm²

We know that:-

• 1 cm² = 0.0001 m²

=> 750cm² = (0.0001 × 750)m² = 0.075m²

Now,

Number of rose beds can be prepared = Area of the triangle field / Area of each rose bed

=> Number of rose beds can be prepared = 33750 / 0.075

=> Number of rose beds can be prepared = 450,000

$\\ \underline{ \rm{ Hence \: \green{ \bold{450,000}} \: rose \: beds \: can \: be \: prepared \: in \: the \: field. }}$

Answer 2

answer is 450,000

follow the above steps