[2 Mark Question Answer]

Question 12 Marks

The perimeter of a square field is numerically equal to its area. Find each side of the square.

Answer

Perimeter of square $=$ Area of square
$\because 4 a=a^2$
$\Rightarrow \frac{a^2}{a}=4$
$\Rightarrow a=4$
$\therefore$ each side of square $=4$

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Question 22 Marks

If A denotes area of a rectangle, l represents its length and $b$ represents its breadth, find:
$b,$ if $A = 88 m^2$ and $l = 8m$

Answer

$b,$ if $A = 88 m^2$ and $l = 8m$
$ b =\frac{ A }{ l } \quad\left[\because A = l \times b \Rightarrow b =\frac{ A }{ l }\right]$
$\Rightarrow b =\frac{88 \ cm ^2}{8 \ cm }=11 m $

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Question 32 Marks

If A denotes area of a rectangle, l represents its length and b represents its breadth, find:
l, if A = 48 cm² and b = 6 cm

Answer

l, if A = 48 cm² and b = 6 cm
$I =\frac{ A }{ b } \quad\left[\because A = l \times b \Rightarrow l =\frac{ A }{ b }\right]$
$\Rightarrow l =\frac{48 cm ^2}{6 cm }=8 cm$

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Question 42 Marks

Find the area of a square, whose side is: 4.1 cm.

Answer

Area of the square = (side)²
= (4.1 cm)²
= 4.1 cm x 4.1 cm
= 16.81 cm²

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Question 52 Marks

Find the area of a square, whose side is: 4.5 cm.

Answer

Area of the square = (side)²
= (4.5 m)²
= 4.5 m x 4.5 m
= 20.25 m²

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Question 62 Marks

Find the area of a square, whose side is: 7.2 cm.

Answer

Area of the square = (side)²
= (7.2 cm)²
= 7.2 cm x 7.2 cm
= 51.84 cm²

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Question 72 Marks

Find the area of a rectangle whose length $= 3.6 m$ breadth $= 90 \ cm$

Answer

length $= 3.6 m$ breadth $= 90 \ cm$
$\Rightarrow $Area of the rectangle $=$ Length $\times$ breadth
$=3.6 m \times 0.9 m \ldots\left[90 \ cm =\frac{90}{100} m =0.9 m \right]$
$=3.24 m ^2$

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Question 82 Marks

Find the area of a rectangle whose length $= 8.5 \ m$ breadth $= 5 \ m.$

Answer

length $= 8.5 \ m$ breadth $= 5 \ m$
$\Rightarrow$ Area of the rectangle $=$ Length $\times$ breadth
$= 8.5 \ m \times 5 \ m$
$= 42.5 \ m^2$

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Question 92 Marks

Find the area of a rectangle whose length $= 15 \ cm$ breadth $= 6.4 \ cm$

Answer

length $= 15 \ cm$ breadth $= 6.4 \ cm$
$\Rightarrow$ Area of the rectangle $=$ Length $\times$ breadth
$= 15 \ cm \times 6.4 \ cm$
$= 96 \ cm^2$

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Question 102 Marks

Find the side of the square whose perimeter is 5 m.

Answer

Perimeter of the square = 5 m
$\therefore$ Its side $=\frac{\text { Perimeter }}{4}$
$=\frac{5}{4} m$
= 1.25 m

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Question 112 Marks

Find the perimeter of a square whose each side is 1.6 m.

Answer

∵ Side of the square = 1.6 m
∴ its perimeter = 4 x side
= 4 x 1.6 m
= 6.4 m

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Question 122 Marks

If P denotes perimeter of a rectangle, l denotes its length and b denotes its breadth, find:
b, if P = 3.2m and l = 100 cm

Answer

b, if P = 3.2m and l = 100 cm
$\left[\therefore 100 cm =\frac{100}{100} m =1 m \right]$
Breadth, $(b)=\frac{P}{2}-1$
$=\frac{3.2}{2} m -1 m$
= 1.6 m - 1 m = 0.6

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Question 132 Marks

If P denotes perimeter of a rectangle, l denotes its length and b denotes its breadth, find:
l, if P = 38cm and b = 7cm

Answer

l, if P = 38cm and b = 7cm
Length, $( I )=\frac{ P }{2}- b$
$=\frac{38}{2}-7 cm$
= 19 cm - 7 cm
= 12 cm

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Question 142 Marks

Find the perimeter of a rectangle whose:
length = 3.6 m and breadth = 2.4 m

Answer

length = 3.6 m and breadth = 2.4 m
∴ Perimeter = 2 (length + breadth)
= 2 (3.6 m + 2.4 m)
= 2 x 6 m = 12 m

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Question 152 Marks

Find the perimeter of a rectangle whose:
length = 10 m and breadth = 8 m

Answer

length = 10 m and breadth = 8 m
∴ Perimeter = 2 (length + breadth)
= 2 (10 m + 8 m)
= 2 x 18 m
= 36 m

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Question 162 Marks

Find the perimeter of a rectangle whose:
length = 40 cm and breadth = 35 cm

Answer

length = 40 cm and breadth = 35 cm
∴Perimeter = 2 (length + breadth)
= 2 (40 cm + 35 cm)
= 2 x 75 cm
= 150 cm
$=\frac{150}{100}$
= 1.5 m

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Question 172 Marks

A regular pentagon of each side 12 cm has same perimeter as that of a regular hexagon. Find the length of each side of the hexagon.

Answer

Perimeter of regular pentagon = 5 x length of the side = 5 x 12 cm = 60 cmClearly, perimeter of the given pentagon = 60 cm⇒ 6 x side of hexagon = 60 cm 60
$\Rightarrow$ side of hexagon $=\frac{60}{6} cm =10 cm$

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Question 182 Marks

A school playground is rectangular in shape with length = 120 m and breadth = 90 m. Some school boys run along the boundary of the play-ground and make 15 complete rounds in 45 minutes. How much distance they run during this period.

Answer

Length of the rectangular playground = 120 mBreadth of the rectangular playground = 90 m
∴ Perimeter of the rectangular ground = 2(l + b)
= 2(120 + 90) m = 420 m
Thus, in one complete round, boys covers a distance of = 420 m
∴ Distance covered in 15 complete rounds = 420 m x 15 = 6300 m

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Question 192 Marks

Each side of a square field is 70 cm. How much distance will a boy walk in order to make?
(i) one complete round of this field?
(ii) 8 complete rounds of this field?

Answer

(i) Distance covered by the boy to make one complete round of the field.
The perimeter of the field: 4 x its side = 4 x 70 = 280 m
(ii) Distance covered by the boy to make 8 complete rounds of this field.
= 280 m x 8 m = 2240 m

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Question 202 Marks

Each side of a square plot of land is 55 m. Find the cost of fencing the plot at the rate of ₹32 per meter.

Answer

∵ Perimeter of square field = 4 x its side = 4 x 55 m
∴ Length of required fencing = 220 m Now, the cost of fencing = its length x its rate
= 220 m x ₹ 32 per metre?
= ₹ 7040

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