Step 3: Enter your full question details here solve this problem (consider 4 squ

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Step 3: Enter your full question details here solve this problem (consider 4 squares of respectives sides a,a+1,a+2.a+3.can we find a so that the area of the largest square is equal to the sum of the areas of the other)
Step 3: Enter your full question details here solve this problem (consider 4 squares of respectives sides a,a+1,a+2.a+3.can we find a so that the area of the largest square is equal to the sum of the areas of the other)
solve this problem (consider 4 squares of respectives sides a,a+1,a+2.a+3.can we find a so that the area of the largest square is equal to the sum of the areas of the other)

Explanation / Answer

area with side a = a^2 area with side a+1 = (a+1)^2 area with side a+2 = (a+2)^2 area with side a+3 = (a+3)^2 (a+3)^2 = (a+2)^2 + (a+1)^2 + a^2 = (a^2 + 4 + 4a) + (a^2 + 1 + 2a ) + a^2 a^2 + 9 + 6a = 3a^2 + 6a + 5 0 = 3a^2 - a^2 + 6a - 6a + 5 -9 = 2a^2 - 4 0 = 2a^2 - 4 4 = 2a^2 4/2 = a^2 = 2 a = sqrt(2) = 1.4142 check: (a+3)^2 = (a+2)^2 + (a+1)^2 + a^2 (sqrt(2) + 3 )^2 = 2 + 9 + 6sqrt(2) = 11 + 6sqrt(2) add these below together: (sqrt(2) + 2)^2 = 2 + 4 + 4sqrt(2) = 6 + 4sqrt(2) (sqrt(2) + 1)^2 = 2 + 1 + 2sqrt(2) = 3 + 2sqrt(2) (sqrt(2))^2 = 2 adding we get, 11 + 6sqrt(2)

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