The perimeter of a rectangle is 14 8 15 cm . If its length is 4 2 3 cm , find its area.

Given length of a rectangle l = 4 2 3 cm Let the breadth of the rectangle is b cm . We know that perimeter of the rectangle is 2 l + b Given perimeter of the rectangle is 14 8 15 cm . ⇒ 2 l + b = 14 8 15 ⇒ 2 4 2 3 + b = 14 8 15 ⇒ 2 4 × 3 + 2 3 + b = 14 × 15 + 8 15 ⇒ 2 12 + 2 3 + b = 210 + 8 15 ⇒ 2 14 3 + b = 218 15 ⇒ 14 3 + b = 218 5 × 1 2 ⇒ b = 218 30 - 14 3 ⇒ b = 218 - 140 30 ⇒ b = 78 30 ⇒ b = 13 5 = 2 3 5 cm We know that area of the rectangle is l × b . ⇒ 4 2 3 × 13 5 ⇒ 4 × 3 + 2 3 × 13 5 ⇒ 14 3 × 13 5 ⇒ 182 15 cm 2 = 12 2 15 cm 2 Hence, the area of the rectangle is 12 2 15 cm 2

EASY

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Find out the length and breadth of inner rectangle in the given figure.

Important Questions on Perimeter and Area

MEDIUM

Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

Find the area of rectangle, whose length is

7 cm

and breadth is

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

Side of a square is first increased by

10 %

and then decreased by

20 %

. What is the overall percentage change in area?

MEDIUM

Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

The perimeter of a rectangle is

60 cm

. If its length is twice its breadth, then its area is:

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

A square park is of side

100 m

. A road

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r m^{2}

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r

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

The area of a square is

144 {cm}^{2}

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

The perimeter of a rectangle ABCD, with length

= 13 cm

and breadth

= 8 cm

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

The diagonal of a square is

24 cm

.What is its perimeter?

MEDIUM

Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

A square park has been divided into two rectangles of equal area. If the perimeter of each of these rectangles is

39 m

, then what will be the perimeter of the square park?

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

What is the area of the largest square which can be inscribed in a circle of radius

28 cm ?

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

What is the area of the largest square which can be inscribed in a circle of radius

14 cm ?

(Take

π = \frac{22}{7}

)

HARD

Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

The perimeter of a rectangle is

14 \frac{8}{15} cm

. If its length is

4 \frac{2}{3} cm

, find its area.

MEDIUM

Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

The respective ratio between the length and breadth of a rectangle is

8 : 5

and its perimeter is

208 cm

. If the side of the square is

40 %

less than the breadth of the rectangle, what is the perimeter of the square?

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

A rectangular plot is

40 m

long and

16 m

broad. A path of uniform width of

2 m

surrounded the plot inside it. Find the cost of paving the road with bricks at

₨ 15

per square meter and also the cost of covering the remaining part of the plot with grass at

₨ 9

per square meter.

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

The area of a square if its perimeter is

64 cm

A {cm}^{2}

. Find the value of

A

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

From a rectangular piece of metal sheet of length and breadth

1 \cdot 60 m and 80 cm

respectively,

3

circular sheets of

20 cm

radius are cut out. If the area of metal left is

A m^{2}

, then what is the value of

A

(Use : π = \frac{22}{7})

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

The length of a rectangle is

10 cm

more than the side of a square and its breath is

8 cm

less than the side of a square. If the areas if both the rectangle and square are equal, then what will perimeter of the rectangle?

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

A rectangle with perimeter

50 cm

has its sides in the ratio

1 : 4

. What is the perimeter of square whose area is same as that of the rectangle?

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

A wire encloses an area of

616 {cm}^{2}

when it is bent in the form of a circle. If the wire is bent in the form of a square, then its area (in

{cm}^{2}

) is very nearly equal to: (Take

π = \frac{22}{7}

)

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Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

If the perimeter of a square plot is the same as that of rectangular plot with side

35 m

and

15 m

. The side of square plot is:

HARD

Mathematics>Geometry>Perimeter and Area>Application of perimeters and area

The length of rectangle is $80 %$ of diagonal of square of area $1225 m^{2}$ , then find area of rectangle, if it's perimeter is $94 \sqrt{2} m$ .

Find out the length and breadth of inner rectangle in the given figure.

Important Questions on Perimeter and Area

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