Question

56.
A square and a rectangle have the same
perimeter. If the side of the square is 16 m
and the length of the rectangle is 18 m, the
breadth of the rectangle is
(A) 14 m
(B) 15 m
(C) 16 m
(D) 17 m
57.
A park is 1500 metres long and 750 metres
wide. A cyclist has to take four rounds of this
park. How much time will he take at the speed
of 4-5 km/h ?
(A) 40 hours (B) 20 hours
(C) 10 hours (D) 4 hours​

Answer 1

1. Given

• A square and rectangle have the same perimeter.
• Side of the square is 16 m
• Length of the rectangle is 18 m

To Find

• The breadth of the rectangle

Solution

First we will find the perimeter of the square field.

Perimeter of Square ⇒ 4 × Side

Side ⇒ 16 m

Perimeter of Given Square ⇒ 4 × 16

Perimeter of Given Square ⇒ 64

Perimeter of Square = Perimeter of Rectangle

Perimeter of Given Rectangle ⇒ 64 m

Perimeter of Rectangle ⇒ 2(Length + Breadth)

Length ⇒ 18 m

Breadth ⇒ x m

Let's solve the following equation to find the breadth

2 (18 + x) = 64

Step 1: Simplify the equation.

⇒ 2 (18 + x) = 64

⇒ 36 + 2x = 64

Step 2: Subtract 36 from both sides of the equation.

⇒ 2x + 36 - 36 = 64 - 36

⇒ 2x = 28

Step 3: Divide 2 from both sides of the equation.

⇒ 2x ÷ 2 = 28 ÷ 2

⇒ x = 14

∴ The breadth of the rectangle is a) 14 m

__________________________

2. Given

• Length of park ⇒ 1500 metres
• Width of park ⇒ 750 metres
• A cyclist takes four rounds of this park
• Speed ⇒ 4.5 km/h

To Find

• The time taken

Solution

First we will find the perimeter of the park. Since the measure of the length and width given aren't equal it is probably a rectangular shaped park.

Perimeter of Rectangle ⇒ 2 (Length + Width)

Length ⇒ 1500 metres

Width ⇒ 750 metres

Perimeter of Given Rectangular Park ⇒ 2 (1500 +750)

Perimeter of Given Rectangular Park ⇒ 2 (2250)

Perimeter of Given Rectangular Park ⇒ 4500 m

∴ The perimeter of given rectangular park is 4500 m

Since the cyclist covers 4 round of the park we will multiply the perimeter obtained to 4 to find the total distance covered.

⇒ 4500 × 4

⇒ 18000 m

∴ The total distance covered by the cyclist is 18000 m

Now we will convert the metres into kilometres

⇒ 1000 m = 1 km

⇒ 18000 ÷ 1000

⇒ 18 km

∴ The total distance covered by the cyclist is 18 km

Time Taken ⇒ Distance (in km) ÷ Speed

Time Taken ⇒ 18 ÷ 4.5

Time Taken ⇒ 4

∴ The time taken by the cyclist to cover 4 rounds of the given park is d) 4 hours.

__________________________

Answer 2

Question No. 1

→ A square and a rectangle have the same  perimeter. If the side of the square is 16 m  and the length of the rectangle is 18 m, the  breadth of the rectangle is

Given :-

→ A square and a rectangle have the same  perimeter.

→ Side of square = 16 m

→ Length of rectangle = 18 m

To Find :-

→ Breadth of the rectangle

Solution :-

→ We are given that ,

$\sf { \fbox{Perimeter\;of\;square\;=\;Perimeter\;of\;rectangle}}$

→ As we know that ,

${\boxed{\sf Perimeter\;of\;a\;square\;= 4 \times Side}}$

${\boxed{\sf Perimeter\;of\;a\;rectangle\;= 2(length+breadth)}}$

$\sf Perimeter\;of\;square = 4 \times Side \\\\\longrightarrow 4 \times 16 \\\\\longrightarrow 64 \; m$

$\sf Perimeter\;of\;Rectangle = 2 (length+breadth)\\\\\longrightarrow 64 \; m = 2 ( 18\;m + breadth)\\\\\longrightarrow (18\;m + breadth) = \dfrac{64}{2} \;m\\\\\longrightarrow (18\;m + breadth) = 32 \; m \\\\\longrightarrow breadth = 32 \; m - 18\; m \\\\\longrightarrow breadth = 14 \; m$

∴ Breadth of the rectangle is 14 m

__________

Question No. 2 :-

→ A park is 1500 meters long and 750 meters  wide. A cyclist has to take four rounds of this  park. How much time will he take at the speed  of 4-5 km/h ?

Given :-

→ Length of the park = 1500 m

→ Breadth of the park = 750 m

→ Speed of Cyclist = 4.5 km/h

To Find :-

→ Total time that will be taken by the cyclist to take four rounds of this park

Solution :-

→ As the cyclist will take round of the park on it's boundary not inside the park . So , we will find perimeter of the park !

→ As we know that

${\boxed{\sf Perimeter\;of\;a\;rectangle\;=\; 2(length+breadth) }}$

$\sf Perimeter\;of\;a\;rectangle\;=\; 2 (length+breadth)\\\\\longrightarrow 2(1500\;m + 750\;m)\\\\\longrightarrow 2(2250\;m)\\\\\longrightarrow 4500\;m$

→  We're given that he need to take four rounds. So, the total distance covered by him will be :

$\sf \longrightarrow 4 \times 4500\;m \\\\\longrightarrow 18000 \; m$

→ Let's convert the total distance covered by him into km

$\sf \rightarrow 1\; m = \dfrac{1}{1000} \;km \\\\\\\rightarrow 18000\;m = \dfrac{18000}{1000} \;km\\\\\\\rightarrow 18\;km$

→ As we know that

${ \boxed{\sf Speed \;=\; \dfrac{Total\;Distance\;Covered}{Total\;time\;taken} }}$

${ \boxed{\sf Total\;time\;taken\;=\; \dfrac{Total\;Distance\;Covered}{Speed} }}$

→ Let's solve now !

$\sf \longrightarrow Total\;Time\;Taken\;=\; \dfrac{Total\;Distance\;Covered}{Speed} \\\\\\\longrightarrow Total\;Time\;taken\;=\; \dfrac{18}{4.5} \\\\\longrightarrow Total\;time\;taken\;=\; 4 \;hours$

∴  Total time that will be taken by the cyclist to take four rounds of this park  is 4 hours .

All Done ! :D