Question

$\huge\sf\fbox\pink{Question}$

The length of a rectangular field is thrice its breadth. If the perimeter is 40 meters, then find the area of the field.

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Answer 1

Answer:

Given :-

• The length of a rectangular field is thrice its breadth.
• The perimeter is 40 metres.

To Find :-

• What is the area of the field.

Solution :-

Let,

$\mapsto \bf Breadth_{(Rectangular\: Field)} =\: a\: m$

$\mapsto \bf Length_{(Rectangular\: Field)} =\: 3a\: m$

As we know that :

$\clubsuit$ Perimeter Of Rectangle Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Perimeter_{(Rectangle)} =\: 2(Length + Breadth)}}}$

According to the question by using the formula we get,

$\implies \sf 40 =\: 2(3a + a)$

$\implies \sf 40 =\: 2(4a)$

$\implies \sf 40 =\: 2 \times 4a$

$\implies \sf 40 =\: 8a$

$\implies \sf \dfrac{\cancel{40}}{\cancel{8}} =\: a$

$\implies \sf \dfrac{5}{1} =\: a$

$\implies \sf 5 =\: a$

$\implies \sf\bold{\purple{a =\: 5}}$

Hence, the required length and breadth of a rectangular field are :

❒ Length Of A Rectangular Field :

$\implies \sf Length_{(Rectangular\: Field)} =\: 3a\: cm$

$\implies \sf Length_{(Rectangular\: Field)} =\: (3 \times 5)\: m$

$\implies \sf\bold{\green{Length_{(Rectangular\: Field)} =\: 15\: m}}$

❒ Breadth Of A Rectangular Field :

$\implies \sf Breadth_{(Rectangular\: Field)} =\: a\: m$

$\implies \sf\bold{\green{Breadth_{(Rectangular\: Field)} =\: 5\: m}}$

Now, we have to find the area of the field :

As we know that :

$\clubsuit$ Area Of Rectangle Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}$

Given :

• Length = 15 m
• Breadth = 5 m

According to the question by using the formula we get,

$\longrightarrow \sf Area_{(Field)} =\: 15 \times 5$

$\longrightarrow \sf\bold{\red{Area_{(Field)} =\: 75\: m^2}}$

${\small{\bold{\underline{\therefore\: The\: area\: of\: the\: field\: is\: 75\: m^2\: .}}}}$

Answer 2

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=> let the breadth if rectangular field be x meters.

☆ Given that:

The length of a rectangular field is thrice its breadth

=> length = 3×breadth

=> length = 3x

☆ perimeter:

=> perimeter = 2(L+B)

=> 40=2(3x+x)

=> 40=2(4x)

=> 40=8x

=> x 40/8

=> x=5

Breadth of rectangular field, x = 5m

Length of rectangular field,3x=3(5)=15m

Therefore, Dimensions of the field are 5 meters and 15 meters respectively

☆ Area of field:

=> Area = L×B

=> Area = 15m×5m

=> Area = 75m2

=> The Area of the rectangular is 75m2.

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