Sum of the areas of two square is468 meter square .If the difference of their perimeter is 24 m. Find the sodes of the two squares
Answers
Let , the sides of first and second square be X and Y.
THEREFORE,
Area of first square = (side)² = (X)² = X²
Area of second square = (side)² = (Y)² = Y².
A/Q,
X² + Y² = 468.....(1)
And,
4X² - 4Y² = 24 .....(2)
From equation (1) we get,
X² = 468-Y² .......(3)
PUTTING THE VALUE OF X² IN EQUATION (2)
4X² - 4Y² = 24
4×(468-Y²) - 4Y² = 24
1872 - 4Y² - 4Y² = 24
-8Y² = 24-1872
-8Y² = -1848
Y² = 1848/8
Y² = 231
Y = ✓231 = 15.18 CM.
Putting the value of Y in equation (3)
X² = 468-Y²
X² = 468 - (15.18)²
X² = 468 - 230.5
X² = 237.5
X= ✓237.5 = 15.4 CM.
HOPE IT WILL HELP YOU... :-)
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 .