Types of Triangles: Using variables

We know that in an equilateral triangle all sides are equal.

Therefore, if we know that one side is equal to X, then all sides are equal to X.

We know that the perimeter of the triangle is 33.

The perimeter of the triangle is equal to the sum of the sides together.

We replace the data:

$x+x+x=33$

$3x=33$

We divide the two sections by 3:

$\frac{3x}{3}=\frac{33}{3}$

$x=11$

We know that the perimeter of a triangle is equal to the sum of all sides together, so we replace the data:

$3x+2x+3.5x=17$

$8.5x=17$

Divide the two sections by 8.5:

$\frac{8.5x}{8.5}=\frac{17}{8.5}$

$x=2$

We use the formula to calculate the area of the right triangle:

$\frac{AC\cdot BC}{2}=\frac{cateto\times cateto}{2}$

And compare the expression with the area of the triangle $6$

$\frac{4\cdot(X-1)}{2}=6$

Multiplying the equation by the common denominator means that we multiply by $2$

$4(X-1)=12$

We distribute the parentheses before the distributive property

$4X-4=12$ / $+4$

$4X=16$ / $:4$

$X=4$

We replace $X=4$ in the expression $BC$ and

find:

$BC=X-1=4-1=3$