Question

Какой длиной могут быть соседние стороны прямоугольникА если сумма их длин 5 см построй один из таких прямоугольникА

Answer 1

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Answer 2

Finding the Length of the Sides of a Rectangle

To find the lengths of the sides of a rectangle when the sum of their lengths is 5 cm, we can use the Pythagorean theorem. The Pythagorean 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.

Using the Pythagorean Theorem

Let's denote the lengths of the sides of the rectangle as a and b. According to the Pythagorean theorem, we have the equation:

a^2 + b^2 = c^2

Where c is the length of the diagonal (hypotenuse) of the rectangle.

Applying the Given Information

Given that the sum of the lengths of the sides is 5 cm, we can express this as:

a + b = 5

Now, we can use these two equations to solve for the lengths of the sides of the rectangle.

Solving for the Lengths of the Sides

We can solve the system of equations using substitution or elimination to find the values of a and b. Let's proceed with substitution.

From the equation a + b = 5, we can express a as 5 - b.

Substituting this into the Pythagorean theorem equation, we get:

(5 - b)^2 + b^2 = c^2

Expanding and simplifying this equation will give us the values of a and b.

Conclusion

By solving the equation (5 - b)^2 + b^2 = c^2, we can find the lengths of the sides of the rectangle when the sum of their lengths is 5 cm.