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:

49:81

Step-by-step explanation:

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

Theorem : The ratio of the areas of the two similar triangle is equal to the square of the perimeter of the corresponding similar triangles .

So, $\frac{\text{Area of} \Delta ABC }{\text{Area of } \Delta PQR} =\frac{(\text{Perimeter of} \Delta ABC)^2 }{(\text{Perimeter of } \Delta PQR)^2}$

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

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

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

Answer 2

Step-by-step explanation:

49:81

Step-by-step explanation:

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

Theorem : The ratio of the areas of the two similar triangle is equal to the square of the perimeter of the corresponding similar triangles .

So, \frac{\text{Area of} \Delta ABC }{\text{Area of } \Delta PQR} =\frac{(\text{Perimeter of} \Delta ABC)^2 }{(\text{Perimeter of } \Delta PQR)^2}

Area of ΔPQR

Area ofΔABC

=

(Perimeter of ΔPQR)

2

(Perimeter ofΔABC)

2

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

Area of ΔPQR

Area ofΔABC

=

(45)

2

(35)

2

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

Area of ΔPQR

Area ofΔABC

=

81

49

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