Question

Треугольник ABC,уголC=90°,cd перпендикуляр ab.bd=16 см CD=12см Найти AC,BC,AB,AD???Срочноо!Геометрияя

Answer 1

СВ=20, квадрат гипотенузы равен сумме квадратов катетов, т.е. СВ^2=CD^2+DB^2
AD=32
AB=48
AC=43

Answer 2

Given Information

We are given a triangle ABC, where angle C is 90°. We also know that CD is perpendicular to AB, BD = 16 cm, and CD = 12 cm. We need to find the lengths of AC, BC, AB, and AD.

Solution

To find the lengths of AC, BC, AB, and AD, we can use the properties of right triangles and apply the Pythagorean theorem.

Let's start by finding the length of AD. Since CD is perpendicular to AB, triangle ACD is a right triangle. We can use the Pythagorean theorem to find AD:

AD^2 = AC^2 - CD^2 Substituting the given values, we have:

AD^2 = AC^2 - 12^2

Next, let's find the length of AB. Since triangle ABC is also a right triangle, we can use the Pythagorean theorem to find AB:

AB^2 = AC^2 + BC^2 Now, let's find the length of BC. Since triangle BCD is a right triangle, we can use the Pythagorean theorem to find BC:

BC^2 = BD^2 - CD^2 Finally, let's find the length of AC. Since triangle ABC is a right triangle, we can use the Pythagorean theorem to find AC:

AC^2 = AB^2 + BC^2

Calculation

Let's substitute the given values into the equations and solve for the unknowns.

From equation (2), we have:

AD^2 = AC^2 - 12^2

From equation (1), we have:

AB^2 = AC^2 + BC^2

From equation (2), we have:

BC^2 = BD^2 - 12^2

From equation (1), we have:

AC^2 = AB^2 + BC^2

Now, let's substitute the given values:

AD^2 = AC^2 - 12^2

AB^2 = AC^2 + BC^2

BC^2 = 16^2 - 12^2

AC^2 = AB^2 + BC^2

Simplifying the equations:

AD^2 = AC^2 - 144

AB^2 = AC^2 + BC^2

BC^2 = 256 - 144

AC^2 = AB^2 + BC^2

Now, let's solve these equations to find the unknowns.

From equation (3), we have:

BC^2 = 256 - 144

Simplifying:

BC^2 = 112

Taking the square root of both sides:

BC = √112

Simplifying:

BC ≈ 10.58 cm

From equation (4), we have:

AC^2 = AB^2 + BC^2

Substituting the value of BC:

AC^2 = AB^2 + (10.58)^2

From equation (1), we have:

AB^2 = AC^2 + BC^2

Substituting the value of BC:

AB^2 = AC^2 + (10.58)^2

Now, let's solve these equations simultaneously to find the values of AC and AB.

Subtracting equation (5) from equation (6), we have:

AC^2 - AB^2 = (10.58)^2 - (10.58)^2

Simplifying:

AC^2 - AB^2 = 0

Factoring:

(AC - AB)(AC + AB) = 0

Since AC and AB cannot be equal to 0, we have:

AC - AB = 0

Simplifying:

AC = AB

Therefore, AC = AB.

Now, let's substitute the value of AC = AB into equation (5) or (6) to find the value of AC or AB.

Using equation (5), we have:

AC^2 = AB^2 + (10.58)^2

Substituting AC = AB:

AB^2 = AB^2 + (10.58)^2

Subtracting AB^2 from both sides:

0 = (10.58)^2

This equation is not possible, as it implies that (10.58)^2 = 0, which is not true.

Therefore, there is no solution for the given values.

Please double-check the given values and ensure they are correct.