Question

Знайдіть площу прямокутника, якщо його периметр дорівнює 14 см, адіагональ 5 см.

Answer 1

А = 3см, в = 4см
S = 3*4=12см²

Answer 2

Finding the Area of a Rectangle

To find the area of a rectangle, we need to know the length of its sides. In this case, we are given the perimeter and the length of the diagonal of the rectangle.

Let's break down the problem step by step:

1. We are given that the perimeter of the rectangle is 14 cm. The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, we have two pairs of equal sides, so we can divide the perimeter by 2 to get the sum of the lengths of two adjacent sides.

The sum of the lengths of two adjacent sides is 14 cm / 2 = 7 cm.

2. We are also given that the length of the diagonal is 5 cm. In a rectangle, the diagonal divides the rectangle into two congruent right triangles. The length of the diagonal, the lengths of the two adjacent sides, and the lengths of the two opposite sides form a right triangle.

Let's use the Pythagorean theorem to find the lengths of the two opposite sides:

- Let's assume the lengths of the two opposite sides are a and b. - According to the Pythagorean theorem, a^2 + b^2 = c^2, where c is the length of the diagonal. - Substituting the values, we have a^2 + b^2 = 5^2.

We don't have enough information to solve for the lengths of the two opposite sides. Therefore, we cannot determine the exact dimensions of the rectangle.

3. However, we can still find the area of the rectangle using the information we have. The area of a rectangle is calculated by multiplying the length and width of the rectangle.

Since we know the sum of the lengths of two adjacent sides is 7 cm, we can assume that the lengths of the two opposite sides are 7 cm and 0 cm. This means that the rectangle is degenerate, with one side having a length of 7 cm and the other side having a length of 0 cm.

Therefore, the area of the rectangle is 7 cm * 0 cm = 0 square cm.

Please note that the assumption made in step 3 is based on the given information and may not represent a physically possible rectangle.