Question

Дано: ДОС и АОВ АО=15; ОД=5; АВ+СД=24; СО:ОВ=1:3. Найти: АВ и СД

Answer 1

Данные треугольники подобны.
ОД/АО=СО/ОВ=СД/АВ=1/3

Имеют коэф. подобия =3
Пусть СД это Х, тогда АВ это 3Х
Составим уравнение:
х+3х=24
4х=24
х=24/4
х=6 - это СД
6*3=18 - это АВ

Ответ: АВ=18, СД=6

Answer 2

Given Information:

We are given the following information: - DOS and AOV are equal to 15. - OD is equal to 5. - AB + CD is equal to 24. - SO:OV is in the ratio 1:3.

Solution:

To find the values of AB and CD, we can use the given information and solve the equations step by step.

Let's start by finding the value of OV. Since SO:OV is in the ratio 1:3, we can write:

OV = (1/4) * SO

Next, we can find the value of SO by subtracting OD from DOS:

SO = DOS - OD

Now, we can substitute the values of SO and OV into the equation AB + CD = 24. Since AB and CD are equal to OV and SO respectively, we can write:

OV + SO = 24

Substituting the values of OV and SO, we get:

(1/4) * SO + SO = 24

Simplifying the equation, we have:

(5/4) * SO = 24

To solve for SO, we can multiply both sides of the equation by (4/5):

SO = (24 * 4) / 5

Now, we can substitute the value of SO back into the equation OV = (1/4) * SO to find OV:

OV = (1/4) * ((24 * 4) / 5)

Finally, we can find the values of AB and CD by substituting the values of OV and SO:

AB = OV = (1/4) * ((24 * 4) / 5)

CD = SO = (24 * 4) / 5

Let's calculate the values:

AB = OV = (1/4) * ((24 * 4) / 5) = 4.8

CD = SO = (24 * 4) / 5 = 19.2

Therefore, the values of AB and CD are 4.8 and 19.2 respectively.

Note: The above calculations are based on the given information and the assumption that the ratios provided are accurate.