Question

Solve for x. Solve for x.

Answer 1

4√3

Explanation:

This is a right triangle. When two sides are given in a right triangle, we need to use the Pythagorean Theorem to solve for the third side.

Pythagorean Theorem: a² + b² = c²

The a here is 11, while the b is x. The c is always the hypotenuse (the longest side), which is 13.

Now we substitute:

11² + x² = 13²

121 + x² = 169

-121 -121

x² = 48

√x² = √48

x = √48 <-- We can simplify that.

√48 = 12 * 4 = 3 * 4 * 4 = 4√3

Answer 2

Hello !

Answer:

`\boxed{\sf x=4\sqrt 3}`

Explanation:

It is a right-angled triangle. To find the value of x, we will have to use the Pythagorean theorem which says that the lengths of the sides of a right-angled triangle satisfy the following equality :

`\boxed{\sf c^2=a^2+b^2}`

Where :

• c represents the length of the hypotenuse.
• a,b represents the lengths of the other two sides.

In this triangle, we can consider a = 11, b = x, and c = 13.

Let's substitute the values of a, b, and c into the formula.

`\sf 13^2=11^2+x^2`

Now we have to solve the equation to find the value of x.

Let's subtract 11² from both sides and calculate.

`\sf 13^2-11^2=11^2-11^2+x^2\\x^2=13^2-11^2\\x^2=169-121\\x^2=48`

Reminder : if x² = a (a ≥ 0), then x = ±√a.

Let's apply that to our equation.

`\sf x=\pm √(48)`

x represents a distance, it must be positive. The unique solution is:

`\sf x=√(48)\\\boxed{\sf x=4\sqrt 3}`

Have a nice day ;)