Right Triangle Area Problem: Solve for X When Area = 6 cm²

Question

Triangle ABC is a right triangle.

The area of the triangle is 6 cm².

Calculate X and the length of the side BC.

00:00 Find X and calculate BC

00:06 (height(AC) times base (BC)) divided by 2

00:14 Substitute appropriate values

00:24 Calculate and solve

00:32 Open parentheses from left to right

00:40 Isolate X

00:47 And this is the size of X

00:49 Q.E.D.1

00:52 Substitute X in side BC

00:59 This is the size of BC

01:01 Q.E.D.2

01:04 And this is the solution to the question

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:

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

X=4, BC=3