Answer:
The corresponding side of the first triangle is 4 m.
Step-by-step explanation:
In similar triangle, ratio of areas of triangles is equal to the ratio of square of their corresponding sides.
Consider, the below two similar triangles,
area(ΔXYZ) = 20m² , area(ΔPQR) = 180m² and PQ = 12m
We have to find value of XY.
According to above property of similar triangle,
[tex]\frac{ar(\bigtriangleup{XYZ})}{ar(\bigtriangleup{PQR})}=\frac{(XY)^2}{(PQ)^2}[/tex]
Put values in the above equation, we get,
[tex]\frac{20}{180}=\frac{(XY)^2}{(12)^2}[/tex]
Solving for XY,
[tex]\Rightarrow \frac{1}{9}=\frac{(XY)^2}{144}[/tex]
Cross multiply, we get,
[tex]\Rightarrow \frac{144}{9}=(XY)^2[/tex]
[tex]\Rightarrow \sqrt{\frac{144}{9}}=(XY)[/tex]
[tex]\Rightarrow \frac{12}{3}=XY[/tex]
[tex]\Rightarrow XY=4[/tex]
Thus, the corresponding side of the first triangle is 4 m.
