हिंदी

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. - Mathematics

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 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.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Quadratic Equations - Exercise 4.11 [पृष्ठ ७१]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 10
अध्याय 4 Quadratic Equations
Exercise 4.11 | Q 7 | पृष्ठ ७१

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.


In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects


Solve for x

`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`


Solve the following quadratic equations by factorization:

`2/2^2-5/x+2=0`


Solve the following quadratic equations by factorization:

a2b2x2 + b2x - a2x - 1 = 0


Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.


Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]


Show that x = −3 is a solution of x2 + 6x + 9 = 0.


The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.


The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.


The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.


Solve equation using factorisation method:

(x + 3)2 – 4(x + 3) – 5 = 0


Solve the following quadratic equation using factorization method:
`"x"^2-11"x"+24=0`


The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.


A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/hr more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.


Solve the following equation by factorization

(x – 3) (2x + 5) = 0


Solve the following equation by factorization 

x2 – (p + q)x + pq = 0


The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.


Solve the following quadratic equation by factorisation method:

x2 + x – 20 = 0


If x = 3 is one root of the quadratic equation 2x2 + px + 30 = 0, find the value of p and the other root of the quadratic equation.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×