Question

Perimeter and Area .....
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Answer 1

$\huge{ \sf{ \underline{ \underline{Question 1.}}}}$

1. The length and the breadth of a rectangular piece ot land are 500 m

respectively.

i) Find( its area)

$\sf{ \underline{ \underline{Solution : - }}}$

From the question it is given that,

Length of the rectangular piece of land = 500 m

Breadth of the rectangular piece of land = 300 m

Then,$\sf \: (i) Area \: of \: rectangle = Length × Breadth \\ \sf= 500 × 300$$\sf \: = 150000 m {}^{2}$

ii) cost of the land for 1 m² or the land = ₹ 10000

$\sf \: = 10000 × 150000 \\ = ₹ 1500000000$

$\sf \: Solution 2: -$

$\sf \: Perimeter \: of \: the \: square \: park = 320 m \\ \sf \: 4 × Lengt h \: of \: the \: side \: of \: park = 320 m$

Then,

$\sf \: Length \: of \: the \: side \: of \: park = \frac{320}{4} \\ \sf= 80 m$

$\sf \: So, \: Area \: of \: the \: square \: park = \\ \sf (length \: of \: the \: side \: of \: park) {}^{2}$$\sf \: = 802</p><p>= 6400 m {}^{2}$

$\huge \sf{ \underline{ \underline{Question \: 3:-}}}$

Find the breadth of a rectangular plot of land, if its area is 440 m2 and the length is 22 m. Also find its perimeter.

$\sf{ \underline{ \underline{Solution}}}$

Area of the rectangular plot = 440 m²

Length of the rectangular plot = 22 m

We know that,

$\sf \: Area \: of \: the \: rectangle = Length × Breadth \\ \sf \: 440 = 22 × Breadth \\ \sf \: Breadth = \frac{440}{22} \\ \sf Breadth = 20 m$

Then,

$\sf \: Perimeter \: of \: the \: rectangle = 2(Length + Breadth) \\ \sf= 2 (22 + 20) \\ \sf= 2(42) \\ \sf= 84 m$

$\sf \: ∴Perimeter \: of \: the \: rectangular \: plot \\ \sf \: is \: 84 \: m.</p><p>$

$\huge \sf{ \underline{ \underline{Question 4.}}}$

The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth.

Also find the area

$\sf { \underline{ \underline{Solution}}}$

Perimeter of the a rectangular sheet = 100 cm

Length of the rectangular sheet = 35 cm

We know that,

Perimeter of the rectangle = 2 (Length + Breadth)

100 = 2 (35 + Breadth)

(100/2) = 35 + Breadth

50 – 35 = Breadth

Breadth = 15 cm

Then,

Area of the rectangle = Length × Breadth

= 35 × 15

= 525 cm²

∴Area of the rectangular sheet is 525 cm²

$\huge \sf{ \underline{ \underline{Question 5.}}}$

The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

$\sf{ \underline{ \underline{Solution}}}$

Area of a square park is the same as of a rectangular park.

Side of the square park = 60 m

Length of the rectangular park = 90 m

We know that,

Area of the square park = (one of the side of

square)²

$\sf= 602</p><p>= 3600 m {}^{2}$

$\sf \: Area \: of \: the \: rectangular \: park = 3600 m {}^{2} … [∵ given]$

$\sf \: Length × Breadth = 3600 \\ \sf \: 90 × Breadth = 3600 \\ \sf Breadth = \frac{3600}{90} \\ \sf \:Breadth = 40 m$

$\huge \sf{ \underline{ \underline{Question 6.}}}$

 A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side?

Also find which shape encloses more area?

$\sf{ \underline{ \underline{Solution}}}$

Length of the rectangle = 40 cm

Breadth of the square = 22 cm

Then,

Perimeter of the rectangle = Perimeter of the Square

$\sf \: 2 (Length + Breadth) = 4 × side$

$\sf \: 2 (40 + 22) = 4 × side$

$\sf \: 2 (62) = 4 × side$

$\sf \: 124 = 4 × side$

$\sf \: Side = \frac{124}{4}$

$\sf \: Side = 31 cm$

$\sf \: So, Area \: of \: the \: rectangle = (Length × Breadth)$$\sf \:= 40 × 22$

$\sf \:= 880 cm {}^{2}$

$\sf \: Area \: of \: square = side {}^{2}$

$\sf \: = 312= 31 × 31= 961 cm {}^{2}$

$\therefore\: Square \: shaped \: wire \: encloses \: more \: area.$

$\huge \sf{ \underline{ \underline{Question 7.}}}$

The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is

30 cm, find its length. Also find the area of the rectangle.$\sf{ \underline{ \underline{Solution}}}$Perimeter of the rectangle = 130 cm

Breadth of the rectangle = 30

We know that,

Perimeter of rectangle = 2 (Length + Breadth)

130 = 2 (length + 30)

$\frac{130}{2} = length + 30$

Length + 30 = 65

Length = 65 – 30

Length = 35 cm

Then,

Area of the rectangle = Length × Breadth

= 35 × 30

= 1050 cm²