Question

The shorter leg is 4. the longer leg is 4 radical 3. The hypotenuse is X

Answer 1

I guess it's worth calculating the value of x

pythagorean theorem since x is the hypotenuse

x²=4²+(4V3)²

x²=16+48

x²=64

x=V64 or -V64

x= 8 or -8

as we are looking for a length and an elongueur is never negative x=8

hypotenuse length: 8

Answer 2

Hello!

Answer:

`\Large \boxed{ \sf x = 8}`

Explanation:

Here is our triangle:

I\
I \
4√3 I \
I \ x
I \
I \

4

We will use the pythagorean theorem.

It is expressed in the following form:

If a triangle is right-angled, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In our triangle, the square of the length of the hypotenuse is:

`\sf x^2`

and the sum of the squares of the lengths of the other two sides is:

`\sf (4√(3))^2 + 4^2`

So we have this equation:

`\sf x^2 = (4√(3))^2 + 4^2`

Let's solve this equation:

`\sf x^2 = (4√(3))^2 + 4^2`

◼ Simplify both sides: **

`\sf x^2 = 48 + 16`

◼ Simplify both sides:

`\sf x^2 = 64`

◼ We know that if
`\sf x^2 = a` , then
`\sf x = \pm√(a)`

`\sf √(x^2) = \pm √(64)`

◼ Simplify both sides:

`\boxed{ \sf x = 8}`

x is not equal to -8 because a length cannot be negative.

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** To simplify
`\sf (4√(3) )^2`, we have this formula:

We know:

`\sf √(x) = x^{(1)/(2)\\\\`

So:

`\sf (√(x) )^2= (x^{(1)/(2)})^2= x^{(2)/(2)} = x^1 = x`

Now:

`\sf (4√(3) )^2 = (4 * √(3))^2 = (4)^2 * (√(3))^2 = 16 * 3 = 48`

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So, the value of x is 8.