Question

I need help please.
Calculate x

Answer 1

The value of x is approximately 3.9.

In triangle ABC, given that angle ABC is a right angle (90 degrees), we can apply the Pythagorean Theorem.

Let BC be the hypotenuse:

`\[ BC^2 = AB^2 + AC^2 \]`

Substitute the known values:

`\[ BC^2 = x^2 + 4^2 \]`

In triangle DAM, with angle ADM as 90 degrees, we can again apply the Pythagorean Theorem to find DM:

`\[ DM^2 = AD^2 + AM^2 \]`

Substitute the known values:

`\[ DM^2 = 2.5^2 + 5^2 \]`

Now, since both triangles share the common point A, we can set the hypotenuses equal to each other:

`\[ BC^2 = DM^2 \]`

Substitute the expressions we found earlier:

`\[ x^2 + 4^2 = 2.5^2 + 5^2 \]`

To solve for x in the equation
`\(x^2 + 4^2 = 2.5^2 + 5^2\)`, follow these steps:

1. Expand and simplify both sides of the equation:

`\[ x^2 + 16 = 6.25 + 25 \]`

2. Combine like terms:

`\[ x^2 + 16 = 31.25 \]`

3. Subtract 16 from both sides to isolate
`\(x^2\)`:

`\[ x^2 = 15.25 \]`

4. Take the square root of both sides:

`\[ x = √(15.25) \]`

5. Simplify the square root:

`\[ x \approx 3.9 \]`

So, the value of x is approximately 3.9.

The probable question may be:

The two triangles ABC and DAM are connected to each other with the common point A. In triangle ABC, angle ABC= 90 degree, AB=x, AC=4. and In triangle DAM, angle ADM= 90 degree, AD=2.5, AM=5. Find the value of x.