Question

The perimeters of two similar triangles ∆ABC and ∆PQR are 35cm and 45cm

respectively, then the ratio of the areas of the two triangles is______________​

Answer 1

Answer:

The ratio of the areas is 49 : 81

Step-by-step explanation:

Given,

Perimeters of ∆ ABC and ∆ PQR are 35cm and 45cm,

Since, the ratio of area of two similar triangles is square of the scalar factor of similarity,

While,

$\text{Scale factor}=\frac{\text{Perimeter of triangle ABC}}{\text{Perimeter of triangle PQR}}$

$=\frac{35}{45}$

$=\frac{7}{9}$

Hence,

$\frac{\text{Area of triangle ABC}}{\text{Area of triangle PQR}}=(\text{Scale factor})^2$

$=(\frac{7}{9})^2$

$=\frac{49}{81}$

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Answer 2

The ratio of the areas of the two triangles is 49:81

Step-by-step explanation:

The perimeters of two similar triangles ∆ABC and ∆PQR are 35cm and 45cm

Theorem : The ratio of the area of two similar triangles is equal to the ratio of the squares of the corresponding perimeter of similar triangles

So, Using Theorem :

$\frac{\text{Area of triangle ABC}}{\text{Area of triangle PQR}}= (\frac{\text{Perimter of triangle ABC}}{\text{Perimeter of triangle PQR}})^2$

$\frac{\text{Area of triangle ABC}}{\text{Area of triangle PQR}}= (\frac{35}{45})^2$

$\frac{\text{Area of triangle ABC}}{\text{Area of triangle PQR}}= (\frac{7}{9})^2$

$\frac{\text{Area of triangle ABC}}{\text{Area of triangle PQR}}= \frac{49}{81}$

Hence The ratio of the areas of the two triangles is 49:81

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The perimeters of two similar triangles ABC and PQR are respectively 36cm and 24cm.If PQ=10cm.Find AB.

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