sum of the area of two square
Answers
EXPLANATION:-
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 = 24, 4(X-Y) = 24
X – Y = 24/4 , X – Y = 6
X = 6+Y ———(3)
Putting the value of X in equation (1)
(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
2Y² + 12Y – 468 +36 = 0
2Y² + 12Y -432 = 0
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
(Y+18) = 0 Or (Y-12) = 0 Y = -18 OR Y = 12
Putting Y = 12 in EQUATION (3)
X = 6+Y = 6+12 = 18
Side of first square = X = 18 m
Side of second square = Y = 12 m.
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