Question

Высота трапеции в 3 раза меньше одного из оснований и в 5 раз меньше другого.Найдите основания и высоту трапеции,если ее площадь равна 100 квадратным сантиметрам

Answer 1

Пущай высота зовется Н

Тогда одно из оснований станет 3Н, а второе 5Н

 

Пишем с этими величинами формулу площади:

 

Н(3Н+5Н)/2 = 100

 

И считаем:

 

четыре Н в квадрате равно 100

Н = корень квадратный из 25

Н=5

 

А раз так, значит малое основание будет 5х3=15, а большое 5х5=25

 

Проверяем:

5(15+25)/2= ровно 100

 

Вот и вся недолга!)

 

 

Ура!))

Answer 2

Understanding the problem

You are given a trapezoid with a certain area and specific height. The height of the trapezoid is three times smaller than one of the bases and five times smaller than the other base. You are asked to find the lengths of the bases and the height of the trapezoid.

Solution

Let's denote the length of the shorter base as b1 and the length of the longer base as b2. The height of the trapezoid is denoted as h.

We are given that the height h is three times smaller than one of the bases, and five times smaller than the other base. Mathematically, this can be represented as:

h = (1/3) * b1

h = (1/5) * b2

We also know that the area of the trapezoid is 100 square centimeters. The formula for the area of a trapezoid is:

Area = (1/2) * (b1 + b2) * h

Substituting the given values, we get:

100 = (1/2) * (b1 + b2) * h

Substituting the values of h from the equations above, we get:

100 = (1/2) * (b1 + b2) * ((1/3) * b1)

Simplifying the equation, we get:

100 = (1/6) * (b1 + b2) * b1

Now, we have two equations:

h = (1/3) * b1

h = (1/5) * b2

And one equation obtained from the area:

100 = (1/6) * (b1 + b2) * b1

We can solve these equations simultaneously to find the values of b1, b2, and h.

Let's substitute the first equation into the second equation:

(1/3) * b1 = (1/5) * b2

This simplifies to:

b2 = (5/3) * b1

Now, substitute this value of b2 into the equation obtained from the area:

100 = (1/6) * (b1 + (5/3) * b1) * b1

Simplifying further:

100 = (1/6) * (8/3) * b1^2

Multiply both sides by 6:

600 = (8/3) * b1^2

Multiply both sides by 3/8:

225 = b1^2

Taking the square root of both sides, we get:

b1 = 15

Substituting this value of b1 into the equation for b2, we get:

b2 = (5/3) * 15 = 25

Finally, substituting b1 into the equation for h, we get:

h = (1/3) * 15 = 5

Therefore, the lengths of the bases are b1 = 15 and b2 = 25, and the height is h = 5.

So, the bases of the trapezoid are 15 cm and 25 cm, and the height is 5 cm.