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.
Let the present age of first friend be x years. So, present age of other be (20 - x).
4 years ago,
Age of first friend = (x – 4) yrs. and age of second friend = (20 – x – 4) yrs = (16 – x) yrs.
According to question,
(x – 4) (16 – x) = 48
⇒ 16 x – x2 – 64 + 4x = 48
⇒ –x2 + 20x – 112 = 0
⇒ x2 – 20x + 112 = 0
Here, a = 1, b = –20, c = 112
Now, D = b2 – 4 ac
= (–20)2 – 4(1) (112) = 400 – 448 = –48
Since, D < 0
So, the given quadratic equation has no real roots and hence it is not possible to calculate the present ages.
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.
Short Answer Type
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