Respuesta :

Firstly, we will have to name vertices

We can see that

triangle ABC and triangle ADE are similar

so, the sides of their ration must be equal

we can write as

[tex] \frac{AD}{AC}=\frac{AE}{AB} [/tex]

now, we can find sides from figure

[tex] AC=9+72 [/tex]

[tex] AD=9 [/tex]

[tex] AE=3x-20 [/tex]

[tex] AB=3x-20+56 [/tex]

now, we can plug these values

[tex] \frac{9}{9+72}=\frac{3x-20}{3x-20+56} [/tex]

now, we can solve for x

[tex] \frac{9}{81}=\frac{3x-20}{3x+36} [/tex]

[tex] \frac{1}{9}=\frac{3x-20}{3x+36} [/tex]

now, we can cross multiply

[tex] 1*(3x+36)=9*(3x-20) [/tex]

[tex] 3x+36=27x-180 [/tex]

we will isolate x terms

[tex] 27x-3x=180+36 [/tex]

[tex] 24x=216 [/tex]

[tex] x=9 [/tex].................Answer


Ver imagen rejkjavik

Answer: The value of x is 9 units.

Step-by-step explanation:

Since we have given that

A triangle with line drawn parallel to the third side and intersecting the other two sides, then the other two sides get divided into equal ratios.

It is also known as "Basic Proportionate theorem"

According to theorem, it becomes,

[tex]\frac{9}{72}=\frac{3x-20}{56}\\\\\frac{1}{8}=\frac{3x-20}{56}\\\\\frac{56}{8}=3x-20\\\\7=3x-20\\\\3x=20+7\\\\3x=27\\\\x=\frac{27}{3}=9\\\\x=9\ units[/tex]

Hence, the value of x is 9 units.

Otras preguntas