Question

Периметр прямоугольника 28см , а его диагональ 10 см. найдите стороны прямоугольника...надо решить через систему уравнений...

Answer 1

пусть стороны прямоугольника a и b

периметр 2(a+b)=28

по теореме Пифагора

a^(2)+b^(2)=100

надо найти a*b

a+b=14   a^+b^+2ab=196

2ab=196-100=96

ab=48

так наверно)

Answer 2

Problem Analysis

We are given the perimeter of a rectangle, which is 28 cm, and the length of its diagonal, which is 10 cm. We need to find the sides of the rectangle using a system of equations.

Solution

Let's assume the length of the rectangle is a and the width is b.

We know that the perimeter of a rectangle is given by the formula: P = 2(a + b).

We also know that the diagonal of a rectangle can be calculated using the Pythagorean theorem: d^2 = a^2 + b^2.

We can set up a system of equations using these two formulas:

Equation 1: P = 2(a + b)

Equation 2: d^2 = a^2 + b^2

Substituting the given values into the equations, we have:

Equation 1: 28 = 2(a + b)

Equation 2: 10^2 = a^2 + b^2

Now we can solve this system of equations to find the values of a and b.

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From Equation 1, we can express a in terms of b:

a = (28 - 2b) / 2

Substituting this value of a into Equation 2, we have:

(28 - 2b)^2 / 4 + b^2 = 100

Expanding and simplifying the equation, we get:

784 - 112b + 4b^2 + 4b^2 = 400

Combining like terms, we have:

8b^2 - 112b + 384 = 0

Dividing the equation by 8, we get:

b^2 - 14b + 48 = 0

Factoring the quadratic equation, we have:

(b - 6)(b - 8) = 0

This gives us two possible values for b: b = 6 or b = 8.

Substituting these values of b back into Equation 1, we can find the corresponding values of a:

For b = 6: a = (28 - 2(6)) / 2 = 8

For b = 8: a = (28 - 2(8)) / 2 = 6

Therefore, the sides of the rectangle are a = 8 cm and b = 6 cm.

Answer

The sides of the rectangle are 8 cm and 6 cm.