Is the sum of the areas of two smaller squares equal to the area of a large square if the side lengths of the squares are 8 feet, 5 feet, and 3 feet? Note that the area of a square is s2, where s is the side length. Explain.

No, the sum of the areas of two smaller squares is not equal to the area of a larger square if the lengths of sides of the squares are 8 feet, 5 feet and 3 feet.

Step-by-step explanation:

WE know that the area of a square is A = s² where s = length of side of the square. Now, since we have squares of varying sides of 8 feet, 5 feet and 3 feet respectively, we want to determine if the areas of the two smaller squares equals that of the larger square. Let A = area of 8 feet side square, A' = area of 5 feet side square and A" = area of 3 feet side square. We want to show if A = A' + A".

Now A = (8 ft)² = 64 ft²

A' = (5 ft)² = 25 ft² and

A" = (3 ft)² = 9 ft²

A' + A" = 25 ft² + 9 ft² = 36 ft²

Since L.H.S = 64 ft²and R.H.S = 36 ft²

So, 64 ft² ≠ 36 ft²

L.H.S ≠ R.H.S

So, the sum of the areas of two smaller squares is not equal to the area of a larger square if the lengths of sides of the squares are 8 feet, 5 feet and 3 feet.