Question

Отрезки АВ и СDпересекаются в точке О и точкой пересечения делятся пополам.АО=37см,СD=94см,а периметр треугольника ВОD равен 159 см.Найдите длину сторона АС.ответ дайте в см Срочнооо!!!ПОМОГИТЕ!!!!ДО ЗАВТРА!!!

Answer 1

94÷2=47см
159-47-37=75см

Answer 2

To find the length of side AC, we can use the information given about the triangle BOD and the fact that AO and CD intersect at point O and divide each other in half.

Let's break down the problem step by step:

1. We are given that AO = 37 cm and CD = 94 cm. 2. We know that AO and CD intersect at point O and divide each other in half. This means that OD = OC = 94/2 = 47 cm. 3. The perimeter of triangle BOD is given as 159 cm. We can use this information to find the length of side BD. - The perimeter of a triangle is the sum of the lengths of its sides. So, BD + BO + OD = 159 cm. - We know that OD = 47 cm, and we need to find the lengths of BD and BO. - Since AO and CD intersect at point O and divide each other in half, we can say that BO = AO = 37 cm. - Substituting the values, we get BD + 37 + 47 = 159 cm. - Simplifying the equation, we find that BD = 159 - 37 - 47 = 75 cm.

Now that we know the length of side BD, we can find the length of side AC.

4. Triangle BOD is similar to triangle AOC because they share the same angle at O and have parallel sides (AO and CD). - Since the triangles are similar, the ratio of their corresponding sides is the same. - The ratio of the lengths of corresponding sides in similar triangles is equal to the ratio of their perimeters. - The perimeter of triangle BOD is 159 cm, and the perimeter of triangle AOC is AC + AO + OC. - Setting up the ratio, we have BD/AC = 159/(AC + 37 + 47). - Substituting the values, we get 75/AC = 159/(AC + 84). - Cross-multiplying, we have 75(AC + 84) = 159AC. - Expanding and simplifying the equation, we find 75AC + 6300 = 159AC. - Rearranging the equation, we get 84AC = 6300. - Dividing both sides by 84, we find AC = 6300/84 = 75 cm.

Therefore, the length of side AC is 75 cm.

Please note that this solution assumes that the given information is accurate and that the triangle BOD is a valid triangle.