Answer:
The corresponding side of the first triangle is 4 m.
Step-by-step explanation:
Area of the first triangle: A1=20 m^2
Area of the second triangle: A2=180 m^2
Lenght of one of the sides of the second triangle: s2=12 m
Corresponding side of the first triangle: s1=?
A1/A2=(s1/s2)^2
Replacing the known values:
(20 m^2)/(180 m^2)=[s1/(12 m)]^2
Simplifying:
2/18=[s1/(12 m)]^2
Simplifying the fraction on the left side of the equation dividing the numerator and denominator by 2:
(2/2)/(18/2)=[s1/(12 m)]^2
1/9=[s1/(12 m)]^2
Solving for s1: Square root both sides of the equation:
sqrt(1/9)=sqrt{[s1/(12 m)]^2}
sqrt(1)/sqrt(9)=s1/(12 m)
1/3=s1/(12 m)
Multiplying both sides of the equation by 12 m:
(12 m)*(1/3)=(12 m)*s1/(12 m)
Simplifying:
(12 m)/3=s1
4 m=s1
s1=4 m
