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

Answer:

56. (A) 14 m

57. (D) 4 hours

Step-by-step explanation:

here, 56) Perimeter of square = 4 × side

                                                  = 4 × 16 m

                                                  = 64 m

now, Perimeter of rectangle = 2 (l + b)

                                     64 m = 2 (18 + b)

                                  64/2 m = 18 + b

                                            b = 32 - 18 m

                                            b = 14 m

57. Perimeter of park (in m) = 2 (l + b)

                                              = 2 (1.5 + 0.75)

                                              = 2 × 2.25

                                              = 4.5 km

now, cyclist take four rounds = 4.5 km × 4

                                                 = 18 km

∴ time = $\frac{distance}{average speed}$

           = $\frac{18 km}{\frac{4+5}{2}}$

           = $\frac{18 km}{\frac{9}{2}}$

           = $\frac{18 * 2}{9}$

           = $\frac{36}{9}$

           = 4 hours

hope it will help you.

Answer 2

Answer ⤵

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

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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.

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