Question

triangle abc is similar to triangle def. the following ratios of corresponding sides are equal.
$\frac{8}{12}=\frac{16}{24}=\frac{2x + 5}{2x+11}$
$x=square$
(type an integer or a simplified fraction.)

Explanation:

Step1: Cross - multiply the ratios

Since $\frac{8}{12}=\frac{2x + 5}{2x+11}$, we have $8(2x + 11)=12(2x + 5)$.

Step2: Expand both sides

Expand the left - hand side: $8\times2x+8\times11 = 16x+88$. Expand the right - hand side: $12\times2x+12\times5=24x + 60$. So, $16x+88=24x + 60$.

Step3: Move the x terms to one side

Subtract $16x$ from both sides: $16x+88-16x=24x + 60-16x$, which gives $88 = 8x+60$.

Step4: Isolate the x term

Subtract 60 from both sides: $88 - 60=8x+60 - 60$, resulting in $28 = 8x$.

Step5: Solve for x

Divide both sides by 8: $x=\frac{28}{8}=\frac{7}{2}$.

Answer:

$\frac{7}{2}$