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8_murik_8 [283]
3 years ago
8

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

Mathematics
2 answers:
soldi70 [24.7K]3 years ago
8 0

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}

IgorC [24]3 years ago
4 0

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}

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