Advertisements
Advertisements
प्रश्न
In Fig. 1, ABCD is a rectangle. Find the value of x and y.
उत्तर
In rectangle ABCD, DC = AB and BC = AD
⇒ x + y = 30 .....(i) and x − y = 14 .....(ii)
Adding (i) and (ii), we get
2x = 44
⇒ x = 22
Put x = 22 in (i), we get y = 8
Hence, x = 22 and y = 8.
APPEARS IN
संबंधित प्रश्न
Solve the following pairs of equations by reducing them to a pair of linear equations
`1/(2x) + 1/(3y) = 2`
`1/(3x) + 1/(2y) = 13/6`
Solve the following pair of linear equations.
152x − 378y = − 74
− 378x + 152y = − 604
A number consist of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.
Seven times a two-digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3. Find the number.
Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is `x/y`
If the numerator is multiplied by 2 and the denominator is reduced by 5, the fraction becomes `6/5`. Thus, we have
`(2x)/(y-5)=6/5`
`⇒ 10x=6(y-5)`
`⇒ 10x=6y-30`
`⇒ 10x-6y+30 =0`
`⇒ 2(5x-3y+15)=0`
`⇒ 5x - 3y+15=0`
If the denominator is doubled and the numerator is increased by 8, the fraction becomes `2/5`. Thus, we have
`(x+8)/(2y)=2/5`
`⇒ 5(x+8)=4y`
`⇒ 5x+40=4y`
`⇒ 5x-4y+40=0`
So, we have two equations
`5x-3y+15=0`
`5x-4y+40=0`
Here x and y are unknowns. We have to solve the above equations for x and y.
By using cross-multiplication, we have
`x/((-3)xx40-(-4)xx15)=-y/(5xx40-5xx15)=1/(5xx(-4)-5xx(-3))`
`⇒ x/(-120+60)=(-y)/(200-75)=1/(-20+15)`
`⇒x/(-60)=-y/125``=1/-5`
`⇒ x= 60/5,y=125/5`
`⇒ x=12,y=25`
Hence, the fraction is `12/25`
If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3. Find the fraction.
Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son. Find their present ages.
Father's age is three times the sum of age of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.
Two years ago, a father was five times as old as his son. Two year later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.
State with reason whether the point (3, −2) will lie on the graph of the equation 5m – 3n = − 21
