Question

сумма оснований трапеции равна 36 сантиметров.диагональ трапеции точкой пересечения с другой диагональю делится в отношении 2:7.найти основания трапеции

Answer 1

Пусть дана трапеция ABCD,  где ВС и AD основания, диагональ BD делится точкой О так, что BO/OD=2/7 .
1) угол СВD=углу BDA (накрет лежащие углы при пересечении параллельных прямых ВС и АД секущей ВД)
2) угол ВСА = углу САД ( накрест лежащие углы при пересечении параллельных прямых ВС и АД секущей СА)

3) РАссмотрим тругольники ВСО и АОД
 а) угол СВД = углу ВДА
 б) угол ВСА = углу САД

 из а и б следует , что тургльники ВСО  и АОД подобные по первому признаку пободия трегольников, значит коэффицент подобия равен  BO/OD=2/7

4) Пусть Вс = 2х, тогда АД = 7 х, ВС+АД = 36
9х=36

х=4

АД = 28, ВС = 8 

Answer 2

Calculation of Trapezoid Bases

To find the lengths of the bases of a trapezoid, we can use the given information about the sum of the bases and the division of the diagonals.

Let's denote the lengths of the bases as a and b.

According to the given information: - The sum of the bases is equal to 36 centimeters. - The diagonal of the trapezoid is divided by the point of intersection with the other diagonal in a ratio of 2:7.

To solve for the lengths of the bases, we can set up the following equations:

1. The sum of the bases: a + b = 36.

2. The ratio of the diagonals: d1/d2 = 2/7.

To find the lengths of the bases, we need to solve these equations simultaneously.

Solving the Equations

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

From equation 1, we can express a in terms of b: a = 36 - b.

Substituting this expression for a into equation 2, we have: (36 - b)/d2 = 2/7.

Now, we can solve for b.

Calculation

Let's solve the equation for b:

(36 - b)/d2 = 2/7.

To simplify the equation, we can cross-multiply:

7(36 - b) = 2d2.

Expanding and rearranging the equation, we get:

252 - 7b = 2d2.

Now, let's solve for b:

7b = 252 - 2d2.

b = (252 - 2d2)/7.

Since we don't have the value of d2, we cannot determine the exact lengths of the bases without additional information.

Please provide the value of d2 or any other relevant information to proceed with the calculation.