Question

What is the value of x?
50pts!

Answer 1

x = 16 (value of x)

x+4 = 16+4 = 20

Explanation:

Hey there! This is a right-triangle because you can see a right-angle (square symbol) there.

Pythagoras Theorem can apply with any right triangles, stating that the sum of adjacent squared and opposite squared equal to hypotenuse squared.

We can express the words above to equation as
`\displaystyle \large{c^2=a^2+b^2}` where c = hypotenuse. For a and b can either be defined as adjacent or opposite.

Adjacent and Opposite are sides that form right angle and Hypotenuse is the longest side and it’s the side that is the opposite of right angle.

From the given attachment, we can conclude that x + 4 is our hypotenuse. Therefore, substitute c = x+4.

`\displaystyle \large{(x+4)^2 = x^2+12^2}`

Using the perfect square formula -
`\displaystyle \large{(x+y)^2 = x^2+2xy+y^2}`

Therefore,
`\displaystyle \large{x^2+2(x)(4)+4^2=x^2+144 \to x^2+8x+16=x^2+144}`

Since the expressions are in quadratic, we will move x²+144 to subtract the left side using transportation property.

`\displaystyle \large{x^2+8x+16-x^2-144=0}\\\displaystyle \large{8x-128=0}\\\displaystyle \large{8x=128}\\\displaystyle \large{(8x)/(8)=(128)/(8)}\\\displaystyle \large{x=16}\\`

Therefore, x = 16 and x+4 is 16+4 = 20.

If you have any questions regarding the Pythagoras Theorem, feel free to ask in comment!