Question

Two corresponding sides of two similar triangles are 3cm and 5cm. The area of the first triangle is 12cm2. What is the area of the second triangle?

Answer 1

Answer:

$33\dfrac{1}{3}\ cm^2$

Step-by-step explanation:

If two corresponding sides of two similar triangles are 3cm and 5cm, then the scale factor is

$k=\dfrac{a_1}{a_2}=\dfrac{3}{5}.$

Two similar triangles have their area proportional with the scale factor of $k^2.$

Hence,

$\dfrac{A_1}{A_2}=k^2,\\ \\\dfrac{12}{A_2}=\left(\dfrac{3}{5}\right)^2,\\ \\\dfrac{12}{A_2}=\dfrac{9}{25},\\ \\A_2=\dfrac{12\cdot 25}{9}=\dfrac{100}{3}=33\dfrac{1}{3}\ cm^2.$