Question

$\huge \tt Question$
1. Perimeter of rectangle is 80 m and its length is 25 m. Find its breadth and area.
2. Find the area and side of square whose perimeter is 84 cm.
3. The supplement of one angle is greater than other by 5 times. Find both angle.
4. Rahul covers along the boundary of a rectangular park of length 50 m and breadth 20. His another friend Sahil cover along boundary of a square park with side 45 m. Find who cover more distance and by how much.
5. A rectangle sheet has a perimeter of 280 cm. The length is 4 times longer than breadth. Find the length and breadth

Answer 1

Answer:

Answer (1)

$\huge\sf \: Given$

• Perimeter of rectangle = 80 cm
• Length of rectangle = 25 cm

$\huge \sf \: To \: Find$

• Breadth of rectangle
• Area of rectangle

$\huge \sf \: Solution$

As we know that

Perimeter of rectangle = 2(l + b)

Let us assume the breadth to be 'x'

80 = 2(25 + x)

80 = (2 × 25) + (2 × x)

80 = 50 + 2x

80 - 50 = 2x

30 = 2x

x = $\dfrac{30}{2}$

x = 15

Therefore :-

Breadth of rectangle is 15 cm

Now,

Let's find Area

As we know that

Area = l × b

Area = 25 × 15

Area = 375 m

Hence,

Area of rectangle is 375 m

Answer (2)

$\huge \sf \: Given$

• Perimeter of square = 84 cm

$\huge \sf \: To \: Find$

• Side
• Area

$\huge \sf \: Solution$

As we know that

Perimeter of square = 4 × side

84 = 4 × side

84 = 4S

S = 84/4

S = 21 cm

Hence the side of square is 21 cm

Now,

Let's find its Area

Area of square = Side²

Area = 21²

Area = 441 cm

Answer (3)

$\huge \sf \: Given$

Supplement of one angle is greater than other by 5 times

$\huge \sf \: To \: Find$

Both sides

$\huge \sf \: Solution$

As we know that sum of supplement angle is 180⁰.

Let's assume the smaller be x and greater side be 5x

180⁰ = x + 5x

180 = 6x

x = 180/6

x = 30

Smaller angle = 30

And,

Greater angle = 5x = 5(30) = 150⁰

Answer (4)

$\huge \sf \: Given$

• Rahul covers along the boundary of a rectangular park of length 50 m and breadth 20m
• Sahil cover along boundary of a square park with side 45 m

$\huge \sf \: To \: Find$

Who cover more distance and by how much

$\huge \sf \: Solution$

Here,

Both have convered boundary. So, we will find perimeter

Distance covered by Rahul

Perimeter of rectangular park = 2(l + b)

Perimeter = 2(50+20)

Perimeter = 2(70)

Perimeter = 140 m

Therefore,

Rahul cover 140 m

Distance covered by Sahil

Perimeter of square park = 4 × Side

Perimeter = 4 × 45

Perimeter = 180 m

Hence :-

Sahil cover more distance by (180 - 140) = 40 m

Answer (5)

$\huge \sf \: Given$

• Perimeter of sheet = 280 cm
• Length is 4 times than its breadth.

$\huge \sf \: To \: Find$

The length and breadth

$\huge \sf \: Solution$

Let the breadth be x cm and length will be 4x

As we know that

Perimeter of sheet = 2(l + b)

280 = (2 × 4x) + (2 × x)

280 = 8x + 2x

280 = 10x

x = $\dfrac{280}{10}$

x = 28

Hence,

Breadth = x = 28 cm

Length = 4x = 4(28) = 112 cm

Extra Formula :-

Perimeter of rectangle = 2(l + b)

Area of rectangle = l × b

Area of square = side²

Perimeter of square = 4 × side