Sum of the areas of two squares is 400m². If the
difference of their perimeter is 16m, find the sides of the
two squares.
Answers
Let the length of each side of a square be x . Then its perimeter = 4x
[Perimeter of a square = 4 × side]
Given : Difference of the perimeters of two squares = 16 m
Perimeter of second square - perimeter of first square = 16
Perimeter of second square - 4x = 16
Perimeter of second square = 16 + 4x
Length of square = perimeter of square/4
Length of each side of second square = (16 + 4x)/4
= 4(4 + x)/4
Length of each side of second square = (4 + x) m
Given : Sum of the area of two squares = 400 m²
Area of first square + Area of second square = 400 m²
x² + (4 + x)² = 400
[Area of a square = side²]
x² + (4)² + x² + 2 × 4 × x = 400
[(a+b)² = a² + b² + 2ab]
2x² + 16 + 8x = 400
2x² + 8x + 16 - 400 = 0
2x² + 8x - 384 = 0
2(x² + 4x - 192) = 0
x² + 4x - 192 = 0
x² + 16x - 12x - 192 = 0
[By middle term splitting]
x(x + 16) - 12 (x + 16) = 0
(x + 16)(x - 12) = 0
(x + 16) = 0 or (x - 12) = 0
x = - 16 or x = 12
Since, side can't be negative ,so x ≠ - 16
Therefore, x = 12
Side of first square = (x) = 12 m
Side of second square = 4 + x
Side of second square = 4 + 12 = 16 m
Side of second square = 16 m
Hence, the side of a square is 12 m and side of second square is 16 m.
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