Rectangle diagonal ratio

The aspect ratio of the rectangle and its diagonal is 9:12:15. Calculate the area of the rectangle if the length of the diagonal is 105 cm.

Final Answer:

a =  63 cm
b =  84 cm

Step-by-step explanation:

$$\begin{gathered} u=105\text{cm} \\ a:b:u=9:12:15 \\ a=9x \\ b=12x \\ u=15x \\ x=u/15=105/15=7\text{cm} \\ a=9\cdot x=9\cdot 7=63\text{cm} \end{gathered}$$

$$\begin{gathered} b=12\cdot x=12\cdot 7=84=84\text{cm} \\ \text{ Verifying Solution: } \\ d=\sqrt{a^2+b^2}=\sqrt{63^2+84^2}=105\text{cm} \\ {d}_2=\sqrt{9^2+12^2}=15\text{x} \end{gathered}$$

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