2 thoughts on “Sum of the areas of two squares is 468 m square if the difference of their perimeter is 24 m find the sides of the two square .”
The Olympic motto “Citius, Altius, Fortius” (“Faster, Higher, Stronger”) was coined by Father Henri Didon, who was a close friend of Baron Pierre de Coubertin. It was adopted by the IOC in 1894.
The Olympic motto “Citius, Altius, Fortius” (“Faster, Higher, Stronger”) was coined by Father Henri Didon, who was a close friend of Baron Pierre de Coubertin. It was adopted by the IOC in 1894.
Answer:
Let the sides of the first and second square be X and Y .
Area of the first square = (X)²
Area of the second square = (Y)²
According to question,
(X)² + (Y)² = 468 m² ——(1).
Perimeter of first square = 4 × X and Perimeter of second square = 4 × Y
According to question,
4X – 4Y = 24 ——–(2)
From equation (2) we get,
4X – 4Y = 244X–4Y=24
4(X-Y) = 244(X−Y)=24
X – Y = 24/4X–Y=24/4
X – Y = 6X–Y=6
X=6+Y———(3)
Putting the value of X in equation (1)
(X)² + (Y)² = 468(X)²+(Y)²=468
= > (6+Y)² + (Y)² = 468
= > (6)² + (Y)² + 2 × 6 × Y + (Y)² = 468
= > 36 + Y² + 12Y + Y² = 468
= > 2( Y² + 6Y – 216) = 0
= > Y² + 6Y – 216 = 0
= > Y² + 18Y – 12Y -216 = 0
= > Y(Y+18) – 12(Y+18) = 0
= > (Y+18) (Y-12) = 0
Putting Y = 12 in EQUATION (3)
X = 6+Y = 6+12 = 18X=6+Y=6+12=18
Side of first square = X = 18 m
Side of second square = Y = 12 m.