Question

The ides of a triangle are 51 cm, 37 cm. and 20 cm. then number of flower beds that can be prepared if each bed is to ocupy 9 sq. m of space is

Answer 1

Question :-

the sides of a triangle are 51 cm, 37 cm. and 20 cm. then number of flower beds that can be prepared if each bed is to occupy 9 sq. cm of space is ?

Given that :-

• the sides of a triangle are 51cm , 37cm and 20cm .
• the area occupy by one flower bed = 9 cm².

Formula used :-

$\sf\: s = \dfrac{a + b + c}{2} \\ \\ \sf \: area \: of \: triangle = \sqrt{s(s - a) \times (s -b ) \times (s- c)}$

where,

• a , b and c are sides of triangle .
• s is semiperimeter .

Solution :-

$\sf \: s \: = \dfrac{a + b +c }{2} \\ \\ \sf \blue\implies \: \frac{51 + 37 + 20}{2} \\ \\ \sf \blue\implies \: \frac{108}{2} = 54 \:c m \: \\ \\ \bf \: s \: = 54 \: cm \: \\ \\ \sf \: area \: of \: triangle = \sqrt{s(s - a) \times (s -b ) \times (s- c)} \\ \\ \sf \: area \: of \: triangle = \sqrt{54(54 - 51) \times (54 - 37) \times (54 - 20)} \\ \\ \sf\blue \implies \: \sqrt{54 \times 3 \times 17 \times 34} \\ \\\sf \blue\implies \: \sqrt{2 \times 3 \times 3 \times 3 \times 3 \times 17 \times 2 \times 17} \\ \\ \sf\blue \implies \:3 \times 3 \times 2 \times 17 \\ \\ \sf \blue\implies \:306 \: {cm}^{2}$

therefore area of triangle = 306 cm²

now,

one flower bed occupy 9cm²

therefore, number of flower bed occupy in 306cm² = 306/9 = 34

therefore 34 flower bed are occupied.