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Is it true, that the sum of areas of two squares with sides 5a and 5b is 25(a + b) (a - b)?

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True

False

answer is B.

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Detailed Solution

Given, two squares with sides 5a and 5b
Sum of these squares is 25(a + b) (a - b).
Area of Square = (side)².

Area of square with side 5a = (5 a) 2 ⇒ Area of square with side 5a = 25 a 2

Area of square with side 5b = (5 b) 2 ⇒ Area of square with side 5b = 25 b 2

Add both areas to find sum of areas and take 25 common.

25 a 2 + 25 b 2 = 25 a 2 + b 2

Use identity

x + y x − y = x 2 − y 2

to simplify given sum of areas.

25 (a + b) (a − b) = 25 (a 2 − b 2)

Compare both the result and conclude that results are not same hence given statement is false.

25 (a 2 + b 2) ≠ 25 (a 2 − b 2)

Hence the sum of areas of two squares with sides 5a and 5b is not 25(a + b) (a - b).
Hence, the correct statement is, the sum of areas of two squares with sides 5a and 5b is 25(

a^{2} + b^{2})

.
So, given statement is false and option 2 is correct.

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