Question

△ABC ≅ △DEF, EF = x 2 - 7, and BC = 4x - 2.

Find the values of x.

(Please Show Work!!!)
Thank You

Answer 1

Therefore the value of x is 5.

Explanation:

Given:

△ABC ≅ △DEF,

EF = x 2 - 7, and

BC = 4x - 2.

To Find:

the values of x. = ?

Solution:

△ABC ≅ △DEF ........Given

If two Triangles are congruent then the Corresponding Parts of Congruent Triangles are Congruent.

∴ BC ≅ EF ...................CPCTC

Substituting the values we get

`4x-2=x^(2)-7\\x^(2)-4x-5=0`

Now By Factorizing we get

`x^(2)-5x+x-5=0\\x(x-5)+1(x-5)=0\\(x+1)(x-5)=0\\x+1=0\ or\ x-5=0\\x=-1\ or\ x=5\\x\ cannot\ be\ negative\\\therefore x=5`

Therefore the value of x is 5.