Sum of the area of two squares is 468 m² . If the difference of their perimeter is 24 m. Find the sides of the two squares.
Answers
STEP 1: Define x
Let the length of one square be x and the other be y.
......................................................................................................................................
STEP 2: Form the equations:
sum of the area of the two squares is 468 m²
⇒ x² + y² = 468
.
Difference in their perimeter is 24 cm
⇒ 4x - 4y = 24
......................................................................................................................................
STEP 3 : Solve x and y:
x² + y² = 468------------------ [ 1 ]
4x - 4y = 24 ------------------ [ 2 ]
.
From [ 2 ]:
4x - 4y = 24
Divide by 4 through:
x - y = 6
Add y to both sides:
x = 6 + y ------------------ [ 3 ]
.
Substitute [ 3 ] into [ 2 ]
(6 + y)² + y² = 468
36 + 12y + y² + y² = 468
2y² + 12y - 431 = 0
y² + 6y - 216 = 0
(y - 12) (y + 18) = 0
y = 12 or y = -18 (rejected, because length cannot be negative)
.
When y = 12 ------------------ Substitute into [ 3 ]
x = 6 + 12
x = 18
.....................................................................................................................................
Answer: The length of the two squares are 12 m and 18 m
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 .