Question

in the diagram below, $overline{ij}paralleloverline{gh}$. find the value of $x$. the diagram is not drawn to scale.

Explanation:

Step1: Apply similar - triangle property

Since $\overline{IJ}\parallel\overline{GH}$, $\triangle FIJ\sim\triangle FGH$. Then, the ratios of corresponding sides are equal. That is, $\frac{FJ}{FH}=\frac{FI}{FG}$.
We know that $FJ = x$, $FH=x + 12$, $FI = 10$, and $FG=10 + 4=14$.
So, $\frac{x}{x + 12}=\frac{10}{14}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{x}{x + 12}=\frac{10}{14}$ gives us $14x=10(x + 12)$.

Step3: Expand and solve for x

Expand the right - hand side: $14x=10x+120$.
Subtract $10x$ from both sides: $14x-10x=10x + 120-10x$, which simplifies to $4x=120$.
Divide both sides by 4: $x = 30$.

Answer:

$30$