Advertisements
Advertisements
प्रश्न
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
Advertisements
उत्तर
Let breadth = x m
then length = (x + 12) m
Area = l × b = x (x + 12) m2
and perimeter
= 2(l + b)
= 2(x + 12 + x)
= 2 (2x + 12) m
According to the condition.
x(x + 12) = 4 x 2(2x + 12)
⇒ x2 + 12x = 16x + 96
⇒ x2 + 12x - 16x - 96 = 0
⇒ x2 - 4x - 96 = 0
⇒ x2 - 12x + 8x - 96 = 0
⇒ x(x - 12) + 8(x - 12) = 0
⇒ (x - 12)(x + 8) = 0
Either x - 12 = 0,
then x = 12
or
x + 8 = 0,
then x = -8,
but it is not possible as it is in negative.
∴ Breadth = 12m
and length = 12 + 12 = 24m.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
6x2 - x - 2 = 0
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
Solve the given quadratic equation for x : 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0 ?
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
Solve the following equation: `"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
Find the factors of the Polynomial 3x2 - 2x - 1.
Solve the following by reducing them to quadratic form:
`sqrt(y + 1) + sqrt(2y - 5) = 3, y ∈ "R".`
Solve the following equation by factorization
x (2x + 1) = 6
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
