A rod 28 centimetres long is to be bent to make a rectangle.Can a rectangle of diagonal 8 centimetres be made?Can a rectangle of diagonal 10 centimetres be made?How about a rectangle of diagonal 14 centimetres?Calculate the lengths of the sides of the rectangles that can be made.
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As per the question,
A rod of length 28 cm is bent to make a rectangle. That mean perimeter of rod is equal to perimeter of rectangle.
Perimeter of rectangle = 2(l + b)
where l = length
b = breadth
Now, the first equation we have:
2(l + b) = 28
l + b = 14
b = (14 - l)
As the diagonal is also given,d = 8 cm
Therefore,
l^{2}+ b^{2} = 8^{2} is the second equation,
substitute the value of b = (14 - l) in l^{2}+ b^{2} = 8^{2}
∴ l^{2} (14-l)^{2} = 8^{2}
l^{2}+14^{2}+l^{2} -28l = 8^{2}
l^{2} +-14l+66=0
As the discriminant is less than 0 that's why a rectangle of a diagonal 8 cm can not be made.
Now for the rectangle to be possible the sum of the length and width is equal to 14.
So one of the possible case is when length = 8 and width = 6.