Please help....

Question

The figure is not drawn to scale. It shows two squares. the total area of two squares is 65 sq cm. the length of the smaller square is more that half the length of the larger square. given that the length of each square is a whole number, find the length of each square.

Answer 1

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Answer 2

a = the length of the larger square

b = the length of the smaller square

a ^ 2 + b ^ 2 = 65

Possible combinations :

a = 1 , b = 8 , a ^ 2 + b ^ 1 = 1 ^ 2 + 8 ^ 2 = 1 + 64 = 65

But the length of the smaller square is greater of the length of the larger square.

You must reject this solution.

a = 4 , b = 7 , a ^ 2 + b ^ 1 = 4 ^ 2 + 7 ^ 2 = 16 + 49 = 65

But the length of the smaller square is greater of the length of the larger square.

You must reject this solution.

a = 7 , b = 4 , a ^ 2 + b ^ 1 = 7 ^ 2 + 4 ^ 2 = 49 + 16 = 65

This is correct solution.

The length of the smaller square is more that half the length of the larger square.

4 > 7 / 2

4 > 3.5

a = 8 , b = 1 , a ^ 2 + b ^ 1 = 8 ^ 2 + 1 ^ 2 = 64 + 1 = 65

But the length of the smaller square is less that half the length of the larger square.

You must reject this solution.

Solution :

a = 7 cm , b = 4 cm