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:
3x2 − 14x − 5 = 0
Divide 57 into two parts whose product is 680.
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]
Find the value of k for which the following equations have real and equal roots:
\[x^2 - 2\left( k + 1 \right)x + k^2 = 0\]
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
The difference of the square of two natural numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
At an annual function of a school, each student gives the gift to every other student. If the number of gifts is 1980, find the number of students.
A school bus transported an excursion party to a picnic spot 150 km away. While returning, it was raining and the bus had to reduce its speed by 5 km/hr, and it took one hour longer to make the return trip. Find the time taken to return.
