Question
The area of a square field is $5184cm^2$. A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.
✓
Answer
First, we have to find the perimeter of the square.
The area of the square is $r^2$, where r is the side of the square.
Then, we have the equation as follows,
$r^2= 5184 = (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times (3 \times 3)$
Taking the square root, we get $r = 2 \times 2 \times 2 \times 3 \times 3 = 72$
Hence the perimeter of the square is $4 \times r = 288m$
Now let L be the length of the rectangular field.
Let W be the width of the rectangular field.
The perimeter is equal to the perimeter of square. Hence, we have,
$2(L + W) = 288$
Moreover, since the length is twice the width,
$L = 2 \times W.$
Substituting this in the previous equation, we get,
$2 \times (2 \times W + W) = 288$
$3 \times W = 144 W$
$= 48$
To find L,
$L = 2 \times W = 2 \times 48 = 96$
Area of the rectangular field $= L \times W = 96 \times 48 = 4608m^2$
The area of the square is $r^2$, where r is the side of the square.
Then, we have the equation as follows,
$r^2= 5184 = (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (3 \times 3) \times (3 \times 3)$
Taking the square root, we get $r = 2 \times 2 \times 2 \times 3 \times 3 = 72$
Hence the perimeter of the square is $4 \times r = 288m$
Now let L be the length of the rectangular field.
Let W be the width of the rectangular field.
The perimeter is equal to the perimeter of square. Hence, we have,
$2(L + W) = 288$
Moreover, since the length is twice the width,
$L = 2 \times W.$
Substituting this in the previous equation, we get,
$2 \times (2 \times W + W) = 288$
$3 \times W = 144 W$
$= 48$
To find L,
$L = 2 \times W = 2 \times 48 = 96$
Area of the rectangular field $= L \times W = 96 \times 48 = 4608m^2$
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