Math, asked by mapth, 1 year ago

the sum of the area of two squares is 468 m^2 and the perimeters are 24 m. tell the sides of the squares?

Answers

Answered by Prakhar2908
1

Given,


Sum of the area of two squares is 468 m^2


Difference between the perimeter of these sqaures is 24 m.


To find ,


length of the sides of these sqaures.


Main solution :-


Let the side of 1st sqaures be equal to x metre.


Let the side of the second sqaure be equal to y metre.


So,


Area of sqaure 1 = x^2


Area of sqaure 2 = y^2


Perimeter of sqaure 1 = 4x


Perimeter of sqaure 2 = 4y


According to question,


x^2 + y^2 = 468 m^2 (i)


4x - 4y = 24m


To find, x and y


4x - 4y = 24


4(x - y) = 24


x -y = 24/4


x-y = 6 (ii)


x = 6 +y (iii)


Putting this in (i)


x^2 + y^2 = 468


(6+y)^2 +y^2 = 468


36 + y^2 + 12 y +y^2 = 468


2y^2 + 12y -432 = 0


2(y^2 +6y -216 ) = 0


y^2 +6y -216 = 0


y^2+18y-12y-216=0


y(y+18)-12(y+18)=0


(y+18)(y-12)=0


Now, y = -18 or y = +12


Since, length can't be negative. We will take only the positive value of y .


Now,


From equation (iii)


x = 6 + y


= 6 + 12


= 18


Answer :- Length of side of one sqaure is 18 m and length of side of other sqaure is 12 m

Answered by Anonymous
1

Step-by-step explanation:

Answer:

→ 18m and 12 m .

Step-by-step explanation:

Let the sides of two squares be x m and y m respectively .

Case 1 .

→ Sum of the areas of two squares is 468 m² .

A/Q,

∵ x² + y² = 468 . ...........(1) .

[ ∵ area of square = side² . ]

Case 2 .

→ The difference of their perimeters is 24 m .

A/Q,

∵ 4x - 4y = 24 .

[ ∵ Perimeter of square = 4 × side . ]

⇒ 4( x - y ) = 24 .

⇒ x - y = 24/4.

⇒ x - y = 6 .

∴ y = x - 6 ..........(2) .

From equation (1) and (2) , we get

∵ x² + ( x - 6 )² = 468 .

⇒ x² + x² - 12x + 36 = 468 .

⇒ 2x² - 12x + 36 - 468 = 0 .

⇒ 2x² - 12x - 432 = 0 .

⇒ 2( x² - 6x - 216 ) = 0 .

⇒ x² - 6x - 216 = 0 .

⇒ x² - 18x + 12x - 216 = 0 .

⇒ x( x - 18 ) + 12( x - 18 ) = 0 .

⇒ ( x + 12 ) ( x - 18 ) = 0 .

⇒ x + 12 = 0 and x - 18 = 0 .

⇒ x = - 12m [ rejected ] . and x = 18m .

∴ x = 18 m .

Put the value of 'x' in equation (2), we get

∵ y = x - 6 .

⇒ y = 18 - 6 .

∴ y = 12 m . .....

Hence, sides of two squares are 18m and 12m respectively .

Similar questions