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:7/9

Step-by-step explanation:

35/45=7/9

Answer 2

Hi,

Answer: 49/81

Step-by-step explanation:

The perimeter of ∆ABC = 35 cm

And,  

The perimeter of ∆PQR = 45 cm

Since, if two triangles are similar then the perimeters of the triangles are proportional to the measures of their corresponding sides.

∴ [Perimeter of (∆ABC)] / [Perimeter of (∆PQR)]

= $\frac{AB}{PQ}$ = $\frac{AC}{PR}$ = $\frac{BC}{QR}$

= $\frac{35}{45}$

= $\frac{7}{9}$

Also, if two triangles are similar then the ratio of the areas of the triangles is equal to the square of ratio of their corresponding sides.

∴ [Area of (∆ABC)] / [Area of (∆PQR)]

= $[\frac{AB}{PQ}]^2$ = $[\frac{AC}{PR}]^2$ = $[\frac{BC}{QR}]^2$

= $[\frac{7}{9}]^2$

= $\frac{49}{81}$

Thus, the ratio of their area is 49/81.

Hope it is helpful!!!!!