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1) A rectangular park is 104m 3long and 56m wide. Anjali walks around it at the rate of 4km/h. What time will she take in making 5 rounds of the park?
2) A wire is in the shape of a regular pentagon of side 12cm. It is rebent into the shape of a rectangle whose length is 3/2 times its bredth. Find the length and the breadth of the rectangle. ​

Answer 1

Question - 1 :

• The length of the rectangular park = 104 m

• The width of the rectangular park = 56 m

The distance she walked for going around the park once is equal to the perimeter of the rectangular park.

Perimeter of the rectangular park = 2(length + breadth)

➙ Perimeter of the rectangular park = 2(104 m + 56 m)

➙ Perimeter of the rectangular park = 2(160 m)

➙ Perimeter of the rectangular park = 320 m

Distance covered for making 5 rounds is equal to 5 times the perimeter of the rectangular park.

➙ Distance covered = 5(320 m)

➙ Distance covered = 1600 m

➙ Distance covered = 1600/1000 km

➙ Distance covered = 1.6 km

$\boxed{\longrightarrow \tt Speed = \dfrac{Distance \ covered}{time \ taken}}$

Speed = 4 km/h

Distance covered = 1.6 km

Time taken = t

Substitute the values,

 $\sf 4 \ km/h=\dfrac{1.6 \ km}{t} \\\\ \sf t=\dfrac{1.6}{4} hr \\\\ \sf t=0.4 \ hr$

 t = 0.4 × 60 min

 t = 24 min

∴ The required time is 24 min

Question - 2 :

• Length of each side of the pentagon = 12 cm
• After bending the wire into the shape of rectangle, length of the rectangle is 3/2 times its breadth

The length of the wire is equal to the perimeter of the pentagon.

➙ Perimeter of the pentagon = 5(side) [since pentagon has 5 sides]

➙ Perimeter of the rectangle = 5(12 cm)

➙ Perimeter of the rectangle = 60 cm

Hence, the length of the wire = 60 cm

Now, the wire is re-bent into the shape of the rectangle.

Let L cm be the it's length and B cm be it's breadth.

As given,  $\sf L=\dfrac{3}{2}B$

 

The length of the wire is equal to the perimeter of the rectangle.

Let's find the perimeter of the rectangle.

Perimeter of the rectangle = 2(length + breadth)

➙ Perimeter of the rectangle = 2(L + B)

➙ Perimeter of the rectangle = 2(3B/2 + B)

➙ Perimeter of the rectangle = 2(5B/2)

➙ Perimeter of the rectangle = 5B cm

The length of the wire is equal to the perimeter of the rectangle.

➛ 60 = 5B

➛ B = 60/5

➛ B = 12 cm

➛ L = 3(12)/2

➛ L = 3(6)

➛ L = 18 cm

Therefore,

The length of the rectangle = 18 cm

The breadth of the rectangle = 12 cm