Question

13. The perimeters of two similar triangles ABC and PQR are 35 cm and 45 cm respectively, then the
ratio of the areas of the two triangles is _
​

Answer 1

Answer:

$\frac{7}{8}$

Step-by-step explanation:

arΔ(abc)/arΔ(PQR) =

$\frac{35}{45 } = \frac{7}{9}$

Answer 2

Step-by-step explanation:

Given The perimeters of two similar triangles ABC and PQR are 35 cm and 45 cm respectively, then the  ratio of the areas of the two triangles is

• According to question triangles ABC and PQR are similar, so the ratio of corresponding sides is same.
• AB / PQ = BC/QR = AC/PR
• Let it be equal to k
• So AB = KPQ
•       BC = KQR
•     AC = KPR
• We know that Perimeter = AB + BC + CA
•                                           = K (PQ + QR + PR)
•                                           = K x perimeter of triangle PQR
• Now K = Perimeter of triangle ABC / Perimeter of triangle PQR
• So AB/PQ = BC/QR = AC/PR = Perimeter of ΔABC / Perimeter of ΔPQR = k
• We know that ratio of area of similar triangles is equal to square of ratio of its corresponding sides.
• So Area of triangle ABC / Area of triangle PQR = (AB / PQ)^2
• So Area of triangle ABC / Area of triangle PQR = (Perimeter of ΔABC / Perimeter of ΔPQR)^2
•                                                                               = (35 / 45)^2
•                                                                                 = (7/9)^2
•                                                                                    = 49 / 81

So the ratio will be 49 : 81

Reference link will be

https://brainly.in/question/12586648

https://brainly.in/question/12606746