Question 2

Mathematics

1 answer:

xz_007 [3.2K]2 years ago

6 0

The correct answer is: x = 8 (Option D)

Explanation:

Given ΔABC≅ΔDFE (Triangle ABC is congruent to triangle DFE).

It means that angle B is congruent to angle F, and C is congruent to E ( likewise A is congruent to D). By using this argument, we can say that, BC≅FE. Consequently, we can safely say that the lengths of those sides are also equal in measure. Therefore,

BC = 20

FE = 3x - 4

Since,

BC = FE (By using congruence statement mentioned above)

20 = 3x - 4

3x = 20+4

3x = 24

x = 8

Hence the correct answer is: x = 8

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$\mathrm{Subtract\:}152\mathrm{\:from\:both\:sides}\\\\19x^2+152-152=0-152\\\\Simplify\ the\ above\ equation\\\\19x^2 = -152\\\\\mathrm{Divide\:both\:sides\:by\:}19\\\\\frac{19x^2}{19} = \frac{-152}{19}\\\\x^2 = -8$

Take square root on both sides

$x = \pm \sqrt{-8}\\\\x = \pm \sqrt{-1}\sqrt{8}\\\\\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i\\\\x = \pm i\sqrt{8}\\\\x = \pm i \sqrt{2 \times 2 \times 2}\\\\x = \pm 2i\sqrt{2}$