Advertisements
Advertisements
प्रश्न
If the perimeter of a rectangular plot is 68 m and the length of its diagonal is 26 m, find its area.
Advertisements
उत्तर
Perimeter = 68 m and diagonal = 26m
Length + breadth = = 34m
Let length = xm
then breadth = (34 – x)m
According to the condition,
l2 + b2 = h2
(x)2 + (34 - x)2 = (26)2
⇒ x2 + 1156 + x2 - 68x = 676
⇒ 2x2 - 68x + 1156 - 676 = 0
⇒ 2x2 - 68x + 480 = 0
⇒ x2 - 34x + 240 = 0 ...(Dividing by 2)
⇒ x2 - 24x - 10x + 240 = 0
⇒ x(x - 24) -10(x - 24) = 0
⇒ (x - 24)(x - 10) = 0
Either x - 24 = 0,
then x = 24
or
x - 10 = 0,
then x = 10
∵ Length is greater than breadth
∴ Length = 24m
and breadth = (34 - 24) = 10m
and Area = l x b = 24 x 10 = 240m2.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0
Solve the following quadratic equation for x:
`x^2+(a/(a+b)+(a+b)/a)x+1=0`
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
Solve the following quadratic equations by factorization:
a2x2 - 3abx + 2b2 = 0
Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
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 equation: 25x (x + 1) = -4
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 equation 3x² – x – 7 = 0 and give your answer correct to two decimal places.
The sum of two numbers is 9 and the sum of their squares is 41. Taking one number as x, form ail equation in x and solve it to find the numbers.
