Math, asked by vennelatharun, 4 months ago

A Wire of length 1m 20cm is cut into two equal pieces. One piece is bent to form a square and the other one bent into form a rectangle of length 22 cm.
i. What is the length of each piece?
a. 10 cm b. 0.6 m
c. 60 cm
d. Both B and C
ii. What measure is breadth of rectangle?
a. 8 cm
b. 16 cm C. 22 cm d. 60 cm
iii. The side of square is
a. 10 cm b. 16 cm
C. 15 cm
d. 14 cm
iv. Area of rectangle is
a. 225 cm b. 225 m²
C. 176 cm?
d. 176 m?
v. Perimeter of square is
a. 60 cm b. 120 cm c. 60 m
d. 240 cm

Answers

Answered by wwwmeghabansal24
1

Answer:

Let the 2 pieces be x,y

Given,

x+y=20

Perimeter of square =x

Side=

4

x

Area of square =

16

x

2

Perimeter of triangle =y

Side=

3

y

Area of triangle =

4

3

(

3

y

)

2

=

36

3

y

2

z= area of square + area of triangle

z=

16

x

2

+

36

3

y

2

z=

16

x

2

+

36

3

(20−x)

2

differentiating the equation, we get,

dx

dz

=

8

x

18

3

(20−x)

equate,

dx

dz

=0

we have,

8

x

18

3

(20−x)

=0

8

x

=

18

3

(20−x)

solving the above equation, we get,

→x=

(9+4

3

)

80

3

y=20−

(9+4

3

)

80

3

→y=

(9+4

3

)

180

dx

2

d

2

z

=

8

1

+

18

3

>0

Thus z is minimum, when x=

(9+4

3

)

80

3

and y=

(9+4

3

)

180

Hence, wire of length 20cm should be cut into pieces of lengths

(9+4

3

)

80

3

,

(9+4

3

)

180

m

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