Advertisements
Advertisements
Question
A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
Advertisements
Solution
Perimeter of rectangle = 44 cm
length + breadth = = 22 cm
Let length = x
then breadth = 22 – x
According to the condition,
x(22 - x) = 105
⇒ 22x - x2 = 105
⇒ x2 - 22x + 105 = 0
⇒ x2 - 15x - 7x + 105 = 0
⇒ x(x - 15) -7(x - 15) = 0
⇒ (x - 15)(x - 7) = 0
Either x - 15 = 0,
then x = 15
or
x - 7 = 0,
then x = 7
As length > breadth,
x = 7 is not admissible.
∴ Length = 15cm
and breadth
= 22 - 15
= 7cm.
APPEARS IN
RELATED QUESTIONS
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
Solve the following quadratic equations by factorization:
`1/(x + 4) - 1/(x - 7) = 11/30, x ≠ 4, 7`
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
The sum of two numbers 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.
Solve the given quadratic equation for x : 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0 ?
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
Solve the following quadratic equations by factorization:
\[\frac{16}{x} - 1 = \frac{15}{x + 1}; x \neq 0, - 1\]
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
If the area of a square is 400 m2, then find the side of the square by the method of factorization.
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
