Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Two natural number differ by 3 and their product is 504. Find the numbers.
Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.
Solve the following quadratic equation using formula method only
x2 - 6x + 4 = 0
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Find two consecutive natural numbers whose squares have the sum 221.
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
Solve the following equation by factorization
x (2x + 1) = 6
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
