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

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vilnius vilnius · Answer 1 · 2018-07-31T09:29:42+02:00

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

[tex] s/s=s^2/s^2 [/tex]

we know that [tex] s^2 [/tex] will be the area of triangle.

[tex] s^2/s^2=75/12 [/tex]

so [tex] s/s=\sqrt{75/12} [/tex]

so the ratio of the perimeter of two triangles will be

[tex] (s+s+s)/(s+s+s)=(\sqrt{75} +\sqrt{75} +\sqrt{75} )/(\sqrt{12}+\sqrt{12} +\sqrt{12} ) [/tex]

ratio of the perimeter=[tex] \sqrt{225} /\sqrt{36} [/tex]

parmesanchilliwack parmesanchilliwack · Answer 2 · 2019-05-21T09:16:20+02:00

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,

[tex]\text{The ratio of their areas}=(\text{The ratio of the perimeter})^2[/tex]

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

So, the ratio of the area = [tex]\frac{75}{12}[/tex]

[tex](\text{The ratio of the perimeter})^2=\frac{75}{12}[/tex]

[tex]\text{The ratio of the perimeter}=\sqrt{\frac{75}{12}}=\sqrt{\frac{25}{4}}=\frac{5}{2}[/tex]