Sum of the areas of two …
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Yogita Ingle 5 years, 8 months ago
Let the sides of first and second square be X and Y .
Area of first square = (X)²
And,
Area of second square = (Y)²
According to question,
(X)² + (Y)² = 544 m² ------------(1).
Perimeter of first square = 4 × X
and,
Perimeter of second square = 4 × Y
According to question,
4X - 4Y = 32 -----------(2)
From equation (2) we get,
4X - 4Y = 32
4(X-Y) = 32
X - Y = 32/4
X - Y = 8
X = 8+Y ---------(3)
Putting the value of X in equation (1)
(X)² + (Y)² = 544
(8+Y)² + (Y)² = 544
(8)² + (Y)² + 2 × 8 × Y + (Y)² = 544
64 + Y² + 16Y + Y² = 544
2Y² + 16Y - 544 +64 = 0
2Y² + 16Y -480 = 0
2( Y² + 8Y - 240) = 0
Y² + 8Y - 240 = 0
Y² + 20Y - 12Y -240 = 0
(Y+20) (Y-12) = 0
(Y+20) = 0 Or (Y-12) = 0
Y = -20 OR Y = 12
Putting Y = 12 in EQUATION (3)
X = 8+Y = 8+12 = 20
Side of first square = X = 20 m
and,
Side of second square = Y = 12 m.
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