Question

Основа рівнобедренного трикутника відноситься до бічної сторони як 16 : 17, а висота, проведена до основи, дорівнює 30 см. Знайдіть сторони трикутника.​

Answer 1

Ответ:

32см,34см

Объяснение:

Answer 2

Finding the sides of an isosceles triangle

To find the sides of an isosceles triangle, we can use the given information about the base and height of the triangle.

Let's denote the length of the base as b and the length of the equal sides as s. According to the given information, the ratio of the base to the equal sides is 16:17, which means that:

b/s = 16/17 We are also given that the height drawn to the base is 30 cm.

To find the lengths of the sides, we can use the Pythagorean theorem. The height of the triangle divides the base into two equal segments, each with a length of b/2.

Using the Pythagorean theorem, we can write the following equation:

s^2 = (b/2)^2 + 30^2 Now, let's solve these equations to find the lengths of the sides.

Solving the equations

First, let's solve the equation b/s = 16/17 for b:

b = (16/17) * s

Substituting this value of b into the equation s^2 = (b/2)^2 + 30^2, we get:

s^2 = ((16/17) * s / 2)^2 + 30^2

Simplifying this equation, we have:

s^2 = (256/289) * s^2 / 4 + 900

Multiplying both sides of the equation by 289 to eliminate the fraction, we get:

289s^2 = (256/4)s^2 + 900 * 289

Simplifying further, we have:

289s^2 = 64s^2 + 260100

Subtracting 64s^2 from both sides of the equation, we get:

225s^2 = 260100

Dividing both sides of the equation by 225, we get:

s^2 = 260100 / 225

Taking the square root of both sides of the equation, we get:

s = sqrt(260100 / 225)

Evaluating this expression, we find that:

s ≈ 18.16 cm

Now, we can substitute this value of s back into the equation b = (16/17) * s to find b:

b = (16/17) * 18.16

Evaluating this expression, we find that:

b ≈ 17.07 cm

Therefore, the lengths of the sides of the triangle are approximately 18.16 cm, 18.16 cm, and 17.07 cm.

Please note that the values provided are approximate due to rounding.

I hope this helps! Let me know if you have any further questions.