Methodsb Draw a square on each sides 3cm×3cm square 4cm×4cm square 5cm×5cmsquare

Question

ScanSolve AI Tutor · Accepted Answer

The method you described is a classic way to demonstrate the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let the sides of the triangle be $a$ , $b$ , and $c$ , where $c$ is the hypotenuse. The theorem is expressed as:

a^2 + b^2 = c^2

Here's how your method applies to the given side lengths:

Calculate the area of the square on the side of length 3 cm.
The area of a square is side $\times$ side.
$A_1 = (3 \text{ cm})^2 = 9 \text{ cm}^2$
Calculate the area of the square on the side of length 4 cm.
$A_2 = (4 \text{ cm})^2 = 16 \text{ cm}^2$
Calculate the area of the square on the side of length 5 cm.
$A_3 = (5 \text{ cm})^2 = 25 \text{ cm}^2$
Verify the Pythagorean theorem by checking if the sum of the areas of the two smaller squares equals the area of the largest square.
$A_1 + A_2 = 9 \text{ cm}^2 + 16 \text{ cm}^2 = 25 \text{ cm}^2$
Since $A_1 + A_2 = A_3$ , the Pythagorean theorem holds for a triangle with sides 3 cm, 4 cm, and 5 cm. This confirms that a triangle with these side lengths is a right-angled triangle.

The sum of the areas of the squares on the two shorter sides is $\boxed{25 \text{ cm}^2}$ .

Methodsb Draw a square on each sides 3cm×3cm square 4cm×4cm square 5cm×5cmsquare

Answer

Step-by-step solution

Calculate the area of the square on the side of length 3 cm.

Calculate the area of the square on the side of length 4 cm.

Calculate the area of the square on the side of length 5 cm.

Verify the Pythagorean theorem by checking if the sum of the areas of the two smaller squares equals the area of the largest square.

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