Question

Two similar triangles have have areas of 75 m2 and 12 m2. find the ratio of the perimeters

Answer 1

we know that having similar triangles so the ratio of sides,area and volume are same.

$s/s=s^2/s^2$

we know that $s^2$ will be the area of triangle.

$s^2/s^2=75/12$

so $s/s=\sqrt{75/12}$

so the ratio of the perimeter of two triangles will be

$(s+s+s)/(s+s+s)=(\sqrt{75} +\sqrt{75} +\sqrt{75} )/(\sqrt{12}+\sqrt{12} +\sqrt{12} )$

ratio of the perimeter=$\sqrt{225} /\sqrt{36}$

Answer 2

Answer:

The ratio of their perimeter is 5 : 2.

Step-by-step explanation:

Since, if two triangles are similar,

Then, the ratio of their area is equal to the square of the ratio of corresponding sides or the ratio of the corresponding perimeters,

$\text{The ratio of their areas}=(\text{The ratio of the perimeter})^2$

Here, the triangles have have areas of 75 m² and 12 m²,

So, the ratio of the area = $\frac{75}{12}$

$(\text{The ratio of the perimeter})^2=\frac{75}{12}$

$\text{The ratio of the perimeter}=\sqrt{\frac{75}{12}}=\sqrt{\frac{25}{4}}=\frac{5}{2}$