Question

Дан прямоугольник ABCD,BD делит прямоугольник пополам,сторона BD равна 25см.Найти сторону AD,если AB:AD=3:4

Answer 1

Вот решение, не откажусь от "лучшего ответа" =3

Answer 2

Understanding the problem

In this problem, we are given a rectangle ABCD, where BD divides the rectangle in half. We are also given that the length of BD is 25 cm. We need to find the length of side AD, given that the ratio of AB to AD is 3:4.

Solution

To solve this problem, we can use the concept of similar triangles. Since BD divides the rectangle ABCD into two congruent triangles, we can consider triangle ABD.

Let's assume that AB is 3x and AD is 4x, where x represents a common factor. We can set up a proportion using the given ratio of AB to AD:

AB / AD = 3 / 4

Substituting the values:

3x / 4x = 3 / 4

Cross-multiplying:

3x * 4 = 4x * 3

12x = 12x

Since both sides of the equation are equal, we can conclude that the value of x does not affect the equality. Therefore, we can solve for x by canceling out the x terms:

12 = 12

This means that x can be any value, as long as both sides of the equation remain equal. Let's assume x = 1 for simplicity.

Substituting x = 1 into the expressions for AB and AD:

AB = 3x = 3 * 1 = 3 cm

AD = 4x = 4 * 1 = 4 cm

Therefore, the length of side AD is 4 cm.