What is the Area of the Green Rectangle?

• Let the length be $(a + b)$ seperated by the line.
• Similarly, let the width be $(c + d)$ .
• The area to find be $A$

$\begin{aligned} \dfrac{a}{b} &= \dfrac{a}{b} \\ \\ \dfrac{a(c)}{b(c)} &= \dfrac{a(d)}{b(d)} \\ \\ \dfrac{12}{8} &= \dfrac{15}{A} \\ \\ A &= 15 \times \dfrac{2}{3} = \boxed{10} \end{aligned}$

First Solution:

Second Solution:

We can use proportionality of Areas: $\frac{12}{8} = \frac{15}{X} \implies X = \frac{15 \times 8}{12} =\boxed{10}$