Question

Tge perimeter of a rectanglar field is 80 m . If the length of the field is decreased by 2m and tge breadtg is increased by 2 m , the area is increased by 36 m square . Find its length and breadth ( HINT : the answer is 30 m , 10 m ) plezz solve it in your copy and send me plezzz plezzz​

Answer 1

Given:

• The perimeter of a rectangular field = 80m

• The length of the field is decreased =2m

• The breadth of the field is increased =2m

• Area is increased =36m²

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To Find :

• It's length and breadth =?

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Solution :

$\bullet\sf \: let \: the \: length \: of \: the \: field = x \\ \sf \: the \: breadth \: of \: the \: field = y \\ \\ \\ \red \bigstar \bf \: perimeter = 2(x + y) = 80 \\ \\ \implies \sf \: perimeter = x + y = \frac{80}{2} \\ \\ \implies \sf \: perimeter = \bf \: x + y = 40 \\ \\ \implies \boxed{ \sf{perimeter = x + y = 40}} \\ \\ \\ \bf \red \bigstar area = xy$

• If the length is decreased by 2m and length is increased by 2m.

•new length=(x-2)

•new breadth =(y+2)

$\implies \sf \: area \: = xy \\ \\ \implies \sf \:area = (x - 2)(y + 2) \\ \\ \implies \sf \: area = xy + 2x - 2y - 4$

This Area is 36m² more than earlier area.

So, we can write

$\\ \implies \sf \: (xy + 2x - 2y - 4) - (xy) = 36 \\ \\ \implies \sf \: 2x - 2y - 4 = 36 \\ \\ \implies \sf \: 2x - 2y = 40 \\ \\ \implies \sf \: x - y = 20$

Adding both linear equations , we get

$\implies \sf \: 2x = 60 \\ \\ \implies \sf x = \frac{60}{2} = 30m \\ \\ \implies \boxed{ \sf{x = 30m}}$

Put x=30m in equation (1)

$\implies \sf \: x + y = 40 \\ \\ \implies \sf \: 30 + y = 40 \\ \\ \implies \sf \: y = 40 - 30 \\ \\ \implies \sf \: y = 10m \\ \\ \implies \boxed{ \sf{y = 10m}}$

Hence, length =30m

Breadth=10m.

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Formulas :

$\bf \red \bigstar \: primeter \: of \: rectangle \: = 2(l + b) \\ \\ \red \bigstar \bf \: area \: of \: rectangle = l \times b$

Answer 2

Answer:

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