Mathematics: Solve for x simplify your radical answer completely. would really appreciate help

Solve for x simplify your radical answer completely.

rodriguezzamyy

28.01.2022

$2\sqrt{13}$

Step-by-step explanation:

Just use the Pythagorean Theorem:

14^2 - 12^2 = x^2

196-144 = x^2

x^2 = 52

$x=\sqrt{52}$

$\sqrt{52} = 2\sqrt{13}$

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tanoah5729

24.11.2022

Possible coordinates of point F are (2,-1) and (6,3).

Step-by-step explanation:

Given two triangles ABC and DEF which are congruent.

we have to find the coordinates of point F while the other are given.

A(1,0), B(-1,2), C(2,3), D(5,0), E(3,2)

Let the coordinates of F are (a,b)

By distance formula,

$BC=\sqrt{(2-(-1))^2+(3-2)^2}=\sqrt{10}$

$AC=\sqrt{(2-1)^2+(3-0)^2}=\sqrt{10}$

∵ ΔABC and ΔDEF are congruent

∴ $BC=\sqrt{10}=FE=\sqrt{(a-3)^2+(b-2)^2}$ → (1)

$AC=\sqrt{10}=FD=\sqrt{(a-5)^2+(b-0)^2}$ → (2)

Now, we will find the value of a and b of system of equation using calculator and we get the coordinates are (2,-1) and (6,3)

Hence, possible coordinates of F are (2,-1) and (6,3).

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