Respuesta :
Answer:
[tex]33\dfrac{1}{3}\ cm^2[/tex]
Step-by-step explanation:
If two corresponding sides of two similar triangles are 3cm and 5cm, then the scale factor is
[tex]k=\dfrac{a_1}{a_2}=\dfrac{3}{5}.[/tex]
Two similar triangles have their area proportional with the scale factor of [tex]k^2.[/tex]
Hence,
[tex]\dfrac{A_1}{A_2}=k^2,\\ \\\dfrac{12}{A_2}=\left(\dfrac{3}{5}\right)^2,\\ \\\dfrac{12}{A_2}=\dfrac{9}{25},\\ \\A_2=\dfrac{12\cdot 25}{9}=\dfrac{100}{3}=33\dfrac{1}{3}\ cm^2.[/tex]
The area of the second triangle is 33.33 square centimeters.
What is the area of a triangle?
When two corresponding sides of two similar triangles are 3cm and 5cm, then the scale factor is;
[tex]\rm Scale \ factor=\dfrac{First \ side}{Second \ side}\\\\Scale \ factor=\dfrac{3}{5}[/tex]
Whenever two triangles are in the same proportionality then the ratio of the area of two triangles is equal to the square of the scale factor.
Therefore,
The area of the second triangle is;
[tex]\rm Scale \ factor=\dfrac{Area \ of \ first \ triangle}{Area \ of \ second \ triangle}\\\\\dfrac{3^2}{5^2}=\dfrac{12}{Area \ of \ second \ triangle}\\\\{Area \ of \ second \ triangle}= \dfrac{12 \times 5^2}{3^2}\\\\{Area \ of \ second \ triangle}= \dfrac{12 \times 5^2}{3^2}\\\\{Area \ of \ second \ triangle}= \dfrac{12 \times 25}{9}\\\\ {Area \ of \ second \ triangle}= \dfrac{300}{9}\\\\{Area \ of \ second \ triangle=33.33[/tex]
Hence, the area of the second triangle is 33.33 square centimeters.
To know more about the Area of the triangle click the link given below.
https://brainly.com/question/17141974
