find the difference of two squares of areas 6:7081 sq.cm and 2:8224 sq.cm
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Step-by-step explanation:
Let the side of the first square be 'a'm and that of the second be 'A' m.
Area of the first square = a² sq m.
Area of the second square = A² sq m. Their perimeters would be 4a and 4A respectively.
Given 4A - 4a = 24 Substituting for A in (2), we get
A - a = 6 - - (1) A ^ 2 + a ^ 2 = 468 - - (2) From (1), A = a + 6
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(a + 6) ^ 2 + a ^ 2 = 468
a ^ 2 + 12a + 36 + a ^ 2 = 468
2a ^ 2 + 12a + 36 = 468
a ^ 2 + 6a + 18 = 234(a + 6) ^ 2 + a ^ 2 = 468
a ^ 2 + 12a + 36 + a ^ 2 = 468
2a ^ 2 + 12a + 36 = 468
a ^ 2 + 6a + 18 = 234
a ^ 2 + 6a - 216 = 0
a ^ 2 + 18a - 12a - 216 = 0
a(a + 18) - 12(a + 18) = 0
(a - 12)(a + 18) = 0
a = 12, - 18
So, the side of the first square is 12 m. and the side of the second square is 18 m.
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