# Rectangular field

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

Result

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

#### Solution:

$u=169 \ \text{m} \ \\ a=12x \ \\ b=5x \ \\ \ \\ u^2=a^2+b^2 \ \\ u^2=(12x)^2+(5x)^2 \ \\ u^2=12^2 \cdot \ x^2+ 5^2 \cdot \ x^2 \ \\ \ \\ x=u / \sqrt{ 12^2 + 5^2 }=169 / \sqrt{ 12^2 + 5^2 }=13 \ \text{m} \ \\ \ \\ a=12 \cdot \ x=12 \cdot \ 13=156 \ \text{m}$
$b=5 \cdot \ x=5 \cdot \ 13=65 \ \text{m}$
$p=2 \cdot \ (a+b)=2 \cdot \ (156+65)=442 \ \text{m}$
$S=a \cdot \ b=156 \cdot \ 65=10140 \ \text{m}^2$

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