Advertisements
Advertisements
Question
The length of verandah is 3m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x, breadth of the verandah write an equation in ‘x’ that represents the above statement.
(ii) Solve the equation obtained in above and hence find the dimension of verandah.
Advertisements
Solution
Let breadth = xm, length = (x + 3)m.
Area = x (x + 3) sq.m.
Perimeter = 2(x + x + 3) = (4x + 6)m.
According to the question, x(x + 3) = 4x + 6
⇒ x2 - x - 6 = 0
⇒ (x + 2) (x ++ 3) = 0
∴ x = 3 and x = -2 (inadmissiable).
Hence breadth = 3m, length = 6m.
RELATED QUESTIONS
The sum of two number a and b is 15, and the sum of their reciprocals `1/a` and `1/b` is 3/10. Find the numbers a and b.
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
Solve the following equation: c
Solve the following quadratic equation using formula method only
6x2 + 7x - 10 = 0
Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:
- the age of the son five years ago.
- the present age of the woman.
Solve the following equation by factorization
2x2 – 8x – 24 = 0 when x∈I
Solve the following equation by factorisation :
x(x + 1) + (x + 2)(x + 3) = 42
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
Solve the following quadratic equation by factorization method.
3p2 + 8p + 5 = 0
The roots of the equation x2 + 3x – 10 = 0 are ______.
