Question

square and a rectangle have same perimeter 40cm and length of the rectangle is 14 cm .which one has maximum area​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

★GIVEN★

Square and a rectangle have same perimeter 40cm and length of the rectangle is 14 cm.

★To Find★

Which one has maximum area.

★SOLUTION★

1)) Area of rectangle:-

• Perimeter of rectangle = 40 cm.
• Length = 14 cm.

$\large{\green{\underline{\boxed{\bf{Perimeter=2(length+breadth)}}}}}$

According to the question,

$\large\implies{\sf{Perimeter=2(length+breadth)}}$

$\large\implies{\sf{40=2(14+b)}}$

$\large\implies{\sf{40=28+2b}}$

$\large\implies{\sf{40-28=2b}}$

$\large\implies{\sf{12=2b}}$

$\large\implies{\sf{\dfrac{12}{2}=b}}$

$\large\implies{\sf{\dfrac{\cancel{12}}{\cancel{2}}=b}}$

$\large\therefore\boxed{\bf{Breadth=6\:cm.}}$

AREA:-

$\large{\green{\underline{\boxed{\bf{Area=Length\times\:Breadth}}}}}$

$\large\implies{\sf{Area=Length\times\:Breadth}}$

$\large\implies{\sf{Area=14\times6}}$

$\large\therefore\boxed{\bf{Area\:of\:rectangle=84\:cm^{2}.}}$

2)) Area of square:-

• Perimeter of square = 40 cm because it is said that square and rectangle have same perimeter.

$\large{\green{\underline{\boxed{\bf{Perimeter=4\times\:side}}}}}$

According to the question,

$\large\implies{\sf{Perimeter=4\times\:side}}$

$\large\implies{\sf{40=side}}$

$\large\implies{\sf{\dfrac{40}{4}=side}}$

$\large\implies{\sf{\dfrac{\cancel{40}}{\cancel{4}}=side}}$

$\large\therefore\boxed{\bf{Side=10\:cm.}}$

AREA:-

$\large{\green{\underline{\boxed{\bf{Area=Side\times\:side}}}}}$

$\large\implies{\sf{Area=Side\times\:side}}$

$\large\implies{\sf{Area=10\times10}}$

$\large\therefore\boxed{\bf{Area\:of\:square=100\:cm^{2}.}}$

As 100 > 84,

Square has maximum area.