Question

Периметр прямокутника дорівнює 46 см, а його площа 120 см2. знайдіть діагональ прямокутника​

Answer 1

Ответ:

P=46 см

S=120 см²

d-?

S=1/2 ×d²

d²= 2s

d=4 корня из 15

Объяснение:

Answer 2

Perimeter and Area of a Rectangle

To find the diagonal of a rectangle, we need to know the perimeter and area of the rectangle. In this case, the perimeter of the rectangle is given as 46 cm and the area is given as 120 cm².

Let's denote the length of the rectangle as L and the width as W.

The perimeter of a rectangle is given by the formula: Perimeter = 2(L + W). And the area of a rectangle is given by the formula: Area = L * W.

We are given that the perimeter is 46 cm, so we can write the equation: 46 = 2(L + W). (Equation 1)

We are also given that the area is 120 cm², so we can write the equation: 120 = L * W. (Equation 2)

Now, we have two equations with two unknowns (L and W). We can solve these equations simultaneously to find the values of L and W.

To solve the equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 1, we can express L in terms of W: L = (46 - 2W) / 2. (Equation 3)

Substituting Equation 3 into Equation 2, we get: 120 = [(46 - 2W) / 2] * W.

Simplifying the equation, we have: 240 = 46W - 2W².

Rearranging the equation, we get a quadratic equation: 2W² - 46W + 240 = 0.

Now, we can solve this quadratic equation to find the values of W. We can use the quadratic formula: W = (-b ± √(b² - 4ac)) / (2a).

For our equation, a = 2, b = -46, and c = 240.

Using the quadratic formula, we find two possible values for W: W₁ and W₂.

Once we have the values of W, we can substitute them back into Equation 3 to find the corresponding values of L.

Finally, we can use the Pythagorean theorem to find the length of the diagonal of the rectangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.

Let's denote the length of the diagonal as D.

Using the values of L and W, we can write the equation: D² = L² + W².

Simplifying the equation, we have: D = √(L² + W²).

By substituting the values of L and W, we can find the length of the diagonal of the rectangle.

Please provide the values of the width and length of the rectangle, and I will calculate the diagonal for you.