Question

The perimeters of two similar triangles are 12cm and
72cm. If the area of smaller triangle is 6 cm
find area of bigger triangle​

Answer 1

Step-by-step explanation:

Given The perimeters of two similar triangles are 12 cm and  72 cm. If the area of smaller triangle is 6 cm  find area of bigger triangle

• Let a,b,c be three side of smaller triangle and ak,bk,ck be three sides of bigger triangle.
• Now a + b + c = 12 and ak + bk + ck = 72
• Now perimeter of smaller triangle = s/2 = 12 / 2 = 6
• Perimeter of bigger triangle = 72 / 2 = 36
• So k(a + b + c) = 72
• Or k = 72 / 12
• Or k = 6
• Area of smaller triangle = √s(s – a)(s-b)(s – c) = 6
•                                      = √6(6 – a)(6 – b)(6 – c) = 6
•                                       = √(6 – a)(6 – b)(6 – c) = 6 / √6
•                                     = (6 – a)(6 – b)(6 – c) = 6-----------------1
• Area of bigger triangle = √36 (36 – a)(36 – b)(36 – c)
•                                     = 6 √6(6 – a) 6(6 – b) 6(6 – c)
•                                     = 6 x 6 √6 x √(6 – a)(6 – b)(6 – c)
•                                   = 6 x 6 √6 x √6 (from 1)
•                                     = 6 x 6 x 6
•                                    = 216 sq cm

Therefore area of bigger triangle is 216 sq cm

Reference link will be

https://brainly.in/question/12586648