Question

1. The sides of triangular field are 41m, 40m and 900cm. Rose beds have to be prepared in
the field. Each rose bed requires 180cm2
of space. How many rose beds can be made in the
field?

Answer 1

Answer:

triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. Wikipedia

Area: ½ × base × height

Perimeter: sum of side lengths of the triangle

Number of vertices: 3

Number of edges: 3

Internal angle: 60° (for equilateral)

Answer 2

Given that :-

• sides of triangular field are 41m , 40m and 900cm .
• one Rose bed requires 180cm² .

here two sides are in meter . firstly we change them into cm .

as we know that,

• 1m = 100cm

therefore,

• 41m = 4100 cm
• 40m = 4000 cm

To find :-

• how many rose beds can be made in the field ?

Formula used :-

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

area of triangle = $\sf \sqrt{s(s - a) \times ( s-b ) \times (s -c )}$

where, s = semiperimeter of the triangle .

Solution :-

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

$\sf \pink\implies \: \: = \dfrac{4100 + 4000 + 900}{2} \\ \\ \sf \pink\implies \: \: = \dfrac{9000}{2} \\ \\ \sf \pink\implies \: \: s = 4500 \: cm \:$

area of triangle = $\sf \sqrt{s(s - a) \times ( s-b ) \times (s -c )}$

$\sf \pink\implies \: \: \sqrt{4500(4500 - 4100) \times (4500 - 4000) \times( 4500 - 900)}$

$\sf \pink\implies \: \: \sqrt{4500 \times 400 \times 500 \times 3600}$

$\sf \pink\implies \: \: \sqrt{3 \times 3 \times 5 \times 100 \times 2 \times 2 \times 100 \times 5 \times 100 \times 2 \times 2 \times 3 \times 3 \times 100}$

$\sf \pink\implies \: \: = 3 \times 5 \times 2 \times 2 \times 3 \times 100 \times 100$

$\sf \pink\implies \: \: 1800000 \: {cm}^{2}$

therefore the area of triangle is

one rose of bed occupy 180cm²

therefore,

the area occupy by the Rose bed in 1800000 cm² is :-

$\sf </strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>\</strong><strong>i</strong><strong>m</strong><strong>p</strong><strong>l</strong><strong>i</strong><strong>e</strong><strong>s</strong><strong> \dfrac{1800000}{180} \\ \\ \sf \: </strong><strong>\red\implies</strong><strong> \dfrac{ \cancel{180}0000}{\cancel{180} } \\ \\ \sf \: </strong><strong>\red\implies</strong><strong> </strong><strong>1000$

hence, the number of rose bed are 1000 .