Short Answer Type
Long Answer TypeIs the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.
Let length of the rectangular park be x m and breadth be y m.
According to question,
perimeter = 80 m ⇒ 2(l + b) = 80 m
⇒ 2 (x + y) = 80
⇒ x + y = 40
⇒ y = 40 – x
i.e., breadth = (40 – x)m
Now, area = 400
⇒ l x b = 400
⇒ x(40 – x) = 400
40x – x2 = 400
⇒ x2 – 40x + 400 = 0
Here, a = 1, b = –40, c = 400
Now, D = b2 – 4ac
= (–40)2 – 4(1) (400) = 1600 – 1600 = 0
Since D = 0
So, the given quadratic equation has equal roots and hence it is possible to design a rectangular park.
Now solving the quadratic equation x2 – 40x + 400 = 0 by quadratic formula, we get
Now, 
Hence, length of the rectangular park (x) = 20 m and breadth = (40 – x) m = 40 – 20 = 20 m.
Short Answer Type
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