Question

Find the value of X.
A.) 2
B.) 4
C.) 6
D.) 8

Answer 1

`x=4`

Explanation:

Given triangle is a right angle triangle

To find out x we use Pythagorean theorem

`c^2=a^2+b^2`

where c is the hypotenuse

c=square root (20),
`a=x and b=x-2`

Plug in the values in the formula

`(√(20) )^2= x^2+(x-2)^2`

`20=x^2+x^2-4x+4`

`20=2x^2-4x+4`

Subtract 20 on both sides

`0=2x^2-4x+-16`

Divide whole equation by 2

0=x^2-2x-8

factor the right hand side

`0=(x-4)(x+2)`

Set each factor =0 and solve for x

`x-4=0` so
`x=4`

`x+2=0` so
`x=-2`

The length x cannot be negative, so
`x=4`