Rectangular field

A rectangular field has a diagonal length of 169m. If the length and width are in the ratio of 12:5. Find the field's dimensions, the field's perimeter, and the field's area.

Correct answer:

a =  156 m
b =  65 m
p =  442 m
S =  10140 m²

Step-by-step explanation:

$$\begin{gathered} u=169\text{m} \\ a=12x \\ b=5x \\ {u}^2=a^2+b^2 \\ {u}^2=(12x{)}^2+(5x{)}^2 \\ {u}^2=12^2\cdot x^2+5^2\cdot x^2 \\ x=u/\sqrt{12^2+5^2}=169/\sqrt{12^2+5^2}=13\text{m} \\ a=12\cdot x=12\cdot 13=156\text{m} \end{gathered}$$

$b=5\cdot x=5\cdot 13=65\text{m}$

$p=2\cdot (a+b)=2\cdot (156+65)=442\text{m}$

$S=a\cdot b=156\cdot 65=10140{\text{m}}^2$

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