Question

A circular wire of radius 4.2 m is cut and bent in the form of a rectangle whose longer side is 20% more than its shorter side. The longer side of the rectangle is :

Answer 1

Answer:

7.1m

Step-by-step explanation:

Radius of circular wire= 4.2m

Circumference of circle= 2πr

2×22/7×4.2= 26.4m

The wire is bent in the form of rectangle

So, the perimeter of the rectangle= 26.4m

Let, Breadth= x

Length( longer side) = 20%+ x

L= 20/100+x

1/5+x= 5x+1/5 = x+1

Perimeter of the rectangle= 2(l+b)

26.4= 2(x+1+x)

26.4= 2(2x+1)

26.4= 4x+2

26.4-2= 4x

24.4= 4x

24.4/4 = x

6.1=x

Breadth= x= 6.1m

Length= x+1= 6.1+1

= 7.1 m

Answer 2

Given data,

radius of circular wire is $R = 4.2 m$

Let, smaller side of the rectangle is $S=x$ meters

given longer side is $20\%$ more than its shorter side, then

longer side of rectangle is

$L = x+(0.2x)\\L = 1.2x$

Now,

NOTE: even though the shape is changed. But, the perimeter is same because the length of wire is not changing.

Therefore, we can write

Perimeter of circle = Perimeter of the rectangle

$2*\pi*R=2(L+S)\\\pi*R=(L+S)\\\pi*4.2=(1.2x+x)\\x= \frac{\pi*4.2}{2.2}\\\\ x=6 m$

if shorter side $S=x=6m$ then the larger side will be

$L = 1.2x \\L=1.2*6\\L = 7.2 m$

∴The longer side of the rectangle is $L = 7.2 m$

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