Question

Меньшее основание равнобедренной трапеции равно боковой стороне. Высота равна 8 см, периметр-52см, а площадь -128 см кв, надите длины сторон трапеции

Answer 1

Трапеция ABCD-равнобедренная,по усл.AB=BC=CD.H=8.P=52.
S=128.по ф-ле S=(BC+AD)÷2·H=128⇒BC+AD=32⇒BC=32-AD.
P=AB+BC+CD+AD=3BC+AD=52⇒3(32-AD)+AD=52⇒AD=22⇒BC=10
Ответ Стороны трапеции равны 22 и 10

Answer 2

Given Information:

We are given the following information about a trapezoid: - The smaller base is equal to one of the lateral sides. - The height is 8 cm. - The perimeter is 52 cm. - The area is 128 cm².

Solution:

To find the lengths of the sides of the trapezoid, we can use the formulas for the perimeter and area of a trapezoid.

Let's denote the lengths of the sides of the trapezoid as follows: - The smaller base: x - The larger base: y - The two lateral sides: a and b

The perimeter of a trapezoid is given by the formula: Perimeter = x + y + a + b

We are given that the perimeter is 52 cm, so we can write the equation: x + y + a + b = 52 The area of a trapezoid is given by the formula: Area = (x + y) * height / 2

We are given that the area is 128 cm² and the height is 8 cm, so we can write the equation: (x + y) * 8 / 2 = 128

Simplifying this equation, we get: x + y = 32 We also know that the smaller base is equal to one of the lateral sides, so we can write the equation: x = a Now we have a system of equations: 1. x + y + a + b = 52 2. x + y = 32 3. x = a

We can solve this system of equations to find the values of x, y, a, and b.

Substituting equation 3 into equation 2, we get: a + y = 32

Substituting equation 3 into equation 1, we get: 2x + y + b = 52

Now we have a new system of equations: 1. a + y = 32 2. 2x + y + b = 52 3. x = a

Substituting equation 3 into equation 1, we get: x + y = 32

Now we have a new system of equations: 1. x + y = 32 2. 2x + y + b = 52 3. x = a

Solving this system of equations, we find: x = 8 y = 24 a = 8 b = 12

Therefore, the lengths of the sides of the trapezoid are: - The smaller base: 8 cm - The larger base: 24 cm - The two lateral sides: 8 cm and 12 cm