Question

A wire in the form of a circle of radius 6 m is bent in the form of a rectangle, whose length and breadth are in the ratio of 8:5. What is the area of the rectangle?

Answer 1

Answer:

Area of rectangle is 15$m^2$

Step-by-step explanation:

Given the wire in form of a circle of radius 6 m

Circumference of circle is calculated as follows

$C = 2 \times \pi \times Radius\\\\C = 2 \times \frac{22}{7} \times 6\\\\C = \frac{264}{7}$

Also, wire is bent to form a rectangle.

Thus, circumference of circle = Perimeter of Rectangle.

Also, Let length of rectangle be $8x$ m

Let Breadth of rectangle be $5x$ m

Thus, perimeter is calculated as follows

$P = 2(\,Length + Breadth)\,\\\\ P = 2(\,8x + 5x)\,\\\\P = 2 \times 13x\\\\P = 26x$

Now, we know

$Perimeter = Circumference\\\\ 26x =  \frac{264}{7}\\\\x = \frac{264}{7 \times 26}x = 1.45 \\\\ x \approx 1.5$

Thus, Length of rectangle $= 8 \times 1.5 = 12$ m

Breadth of rectangle $= 5 \times 1.5 = 7.5$ m

Thus, Area of rectangle is calculated as

$Area = Length \times Breadth \\\\ Area = 12 \times 7.5\\\\Area = 15\hspace{0.1cm}m^2$

Answer 2

The answer is 78.4 m²

GIVEN

A wire in the form of a circle of radius 6 m is bent in the form of a rectangle, whose length and breadth are in the ratio of 8:5.

TO FIND

The area of the rectangle.

SOLUTION

We can simply solve the above problem as follows;

We know that,

Circumference of the circle = Perimeter of the rectangle.

Circumference = 2πr = 2 × 3.14 × 6 = 37.68 m

Let the length of the rectangle = 8x

Breath of the rectangle = 5x

Now,

Perimeter of the rectangle = 2 (l + b)

2(8x + 5x) = 37.68

26x = 37.68

x = 37.68/26 = 1.4

Therefore,

Length of the rectangle = 8 × 1.4 = 11.2 meters

Breath of the rectangle = 5 × 1.4 = 7 meters

Area of the rectangle = l × b

= 11.2 × 7

= 78.4 m²

Hence, The answer is 78.4 m²

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