Advertisements
Advertisements
प्रश्न
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
Advertisements
उत्तर
Let the sides of the squares are x m and = y m.Then
According to question,
Sum of the difference of their perimeter=64 m
4x - 4y = 64
x - y = 16
y = x - 16 .................... (1)
And sum of the areas of square = 640 m2
x2 + y2 = 640 ............ (2)
Putting the value of x in equation (2) from equation (1)
x2 + (x - 16)2 = 640
x2 + x2 - 32x + 256 = 640
2x2 - 32x + 256 - 640 = 0
2x2 - 32x - 384 = 0
2(x2 - 16x - 192) = 0
x2 - 16x - 192 = 0
x2 - 24x + 8x - 192 = 0
x(x - 24) + 8(x - 24) = 0
(x - 24)(x + 8) = 0
x - 24 = 0
x = 24
or
x + 8 = 0
x = -8
Sides of the square never are negative.
Therefore, putting the value of x in equation (1)
y = x - 16 = 24 - 16 = 8
Hence, sides of the square be 24m and 8m respectively.
APPEARS IN
संबंधित प्रश्न
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
The sum of the squares of three consecutive natural numbers as 149. Find the numbers
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
Solve the following quadratic equations by factorization:
`4/(x+2)-1/(x+3)=4/(2x+1)`
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
Solve the following quadratic equations by factorization: \[\frac{1}{2a + b + 2x} = \frac{1}{2a} + \frac{1}{b} + \frac{1}{2x}\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[kx\left( x - 2\sqrt{5} \right) + 10 = 0\]
If the equation x2 + 4x + k = 0 has real and distinct roots, then
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
If the sum and product of the roots of the equation kx2 + 6x + 4k = 0 are real, then k =
Solve the following equation : `"ax"^2 + (4"a"^2 - 3"b")"x" - 12"ab" = 0`
A two digit number is such that the product of the digit is 12. When 36 is added to the number, the digits interchange their places. Find the numbers.
The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm2, find the hypotenuse.
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
Solve the following equation by factorization
`sqrt(3x + 4) = x`
Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )2 + 6(3x + 1) – 8 = 0
Find two consecutive natural numbers such that the sum of their squares is 61.
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.
