Advertisements
Advertisements
Question
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
Solution
Let the side of the larger square be x and the side of the smaller square be y.
The sum of the areas is 640 m2.
x2 + y2 = 640 ...(1)
The difference of their perimeters (4 × side) is 64 m.
4x − 4y = 64
4(x − y) = 64
x − y = `64/4`
x − y = 16
x = y + 16 ...(2)
Putting the value of x in equation (2) from equation (1).
(y + 16)2 + y2 = 640
(y2 + 32y + 256) + y2 = 640
2y2 + 32y + 256 − 640 = 0
2y2 + 32y − 384 = 0
Divide the entire equation by 2 to simplify:
y2 + 16y − 192 = 0
y2 + 24y − 8y − 192 = 0
y2 + 24y − 8y − 192 = 0
y(y + 24) − 8(y + 24) = 0
(y + 24) (y − 8) = 0
y + 24 = 0 or y − 8 = 0
y = −24 or y = 8
Sides of the square are never negative.
∴ y = 8
∴ Side of the smaller square y = 8 m
Side of the larger square y + 16
= 8 + 16
= 24 m
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
x2 – 3x – 10 = 0
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.
Solve the following quadratic equations by factorization:
`(x+3)/(x+2)=(3x-7)/(2x-3)`
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
Solve the following quadratic equations by factorization:
a2b2x2 + b2x - a2x - 1 = 0
Find the consecutive numbers whose squares have the sum 85.
A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number
Solve the following quadratic equation by factorisation.
2m (m − 24) = 50
Find the value of k for which the following equations have real and equal roots:
\[x^2 - 2\left( k + 1 \right)x + k^2 = 0\]
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
Solve the following equation by factorization
2x2 – 8x – 24 = 0 when x∈I
Solve the following equation by factorization
a2x2 + (a2+ b2)x + b2 = 0, a ≠ 0
Solve the following equation by factorization
`(8)/(x + 3) - (3)/(2 - x)` = 2
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.
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
If `x + 1/x = 2.5`, the value of x is ______.
If x4 – 5x2 + 4 = 0; the values of x are ______.
