Question

1)A piece of a string is 48cm long. What will be the length of each side of the string is used to form:

a)A square b)An equilateral triangle c)A regular hexagon.

2) How many envelopes can be made out of a sheet of paper 125cm by 85cm supposing each envelope requires a piece of paper of size 17cm by 5cm?

3) Anil runs around a square field of side 60m four times. What distance does he cover? Vinay runs twice a rectangular with length field 180m and breadth 110m. What distance does he cover? Who covers more distance and by how much?

Answer 1

Explanation:

The string length is the perimeter of the shape.

∴ For each case, perimeter=30cm

(i) Square

A square has all the side equal.

Perimeter=4×(side of square)

∴side of square=

4

perimeter

​

=

4

30

​

=7.5cm

Hence, length of each side if the string is used to form a square will be 7.5 cm.

(ii) Equilateral triangle

An equilateral triangle has three equal sides.

Perimeter=3×(side)

∴side=

3

perimeter

​

=

3

30

​

=10cm

Hence, length of each side if the string is used to form an equilateral triangle will be 10 cm.

(iii) Regular hexagon

A regular hexagon has six equal sides.

Perimeter=6×(side)

∴side=

6

perimeter

​

=

6

30

​

=5cm

Hence, length of each side if the string is used to form a regular hexagon will be 5 cm

Answer 2

square 12cm

triangle 16cm

regular hexagon 9.6 cm

Given length of the sheet of paper = 125 cm Also given that breadth of the sheet of paper = 85 cm Area of a sheet of paper = Length x Breadth = 125 cm x 85 cm = 10,625 cm2 Length of sheet required for an envelope = 17 cm Breadth of sheet required for an envelope = 5 cm Area of the sheet required for one envelope = Length x Breadth = 17 cm x 5 cm = 85 c m2 Thus, required number of envelopes = 10,625/85 = 125

Perimeter of square field = Distance

Perimeter = 4s = 60 x 4 = 240m

Anil ran around the field 4 times. So, 240 x 4 = 960m

Anil ran 960 meters

Perimeter of rectangle = Distance

Perimeter = 2 (1 + b) = 2 (180 + 110) = 2 x 290 =

580m

Vinay ran around 2 times

So, 580 x 2 = 1160 meters

Now, 1160 - 960 = 200m

Thus, Vinay ran 200 meters more than Anil.