Question

Площа прямокутника дорівнює 42см² а його периметр 26см.Знайдіть сторони прямокутника​

Answer 1

Объяснение:

Дано

S=42см²

Р=26см

Найти

a=?

b=?

Решение

S=a×b; 42=a×b

P=2×(a+b);

26=2×(a+b)

13=a+b

a=13-b

42=(13-b)×b

42=13b-b²

b²-13b+42=0

D=169-168=1

b1=(13+1)÷2=7см

b2=(13-1)÷2=6см

a1=13-7=6см

а2=13-6=7см

Ответ: 6см и 7см

Answer 2

Finding the Sides of a Rectangle

To find the sides of a rectangle when given the area and perimeter, we can use the following formulas:

1. Area of a Rectangle (A) = length (l) * width (w) 2. Perimeter of a Rectangle (P) = 2 * (length + width)

We are given: - Area (A) = 42 cm² - Perimeter (P) = 26 cm

Calculating the Sides

Let's use the given information to calculate the sides of the rectangle.

First, we can find the sides of the rectangle by solving the system of equations formed by the area and perimeter.

From the perimeter equation: 26 = 2 * (l + w) => l + w = 13

We can express one of the variables in terms of the other: l = 13 - w

Now, using the area equation: 42 = l * w => 42 = (13 - w) * w => 42 = 13w - w²

This is a quadratic equation, and we can solve for the sides of the rectangle using the quadratic formula.

Quadratic Formula

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / (2a)

In this case, the quadratic equation is in the form ax² + bx + c = 0, where: - a = -1 - b = 13 - c = -42

Using the quadratic formula, we can find the values of w (width) and l (length).

Solution

After solving the quadratic equation, we find that the sides of the rectangle are approximately: - Width (w) ≈ 6 cm - Length (l) ≈ 7 cm

Therefore, the sides of the rectangle are approximately 6 cm and 7 cm.