Question

the perimeters of two similar triangles are 12 cm and 72 cm . If the area of smaller triangle is 6cm², find the area of bigger triangle?
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Answer 1

Answer:

As we know that the ratios of the two corresponding sides of a two similar traingles is equal to  the ratio of their perimeter

Also the ratio of the areas of the two similar triangle is equal to the square of the ratio of their corresponding sides

then ,

let the area of the bigger traingle is x

therefore

according to the question

then

x = 36 × 6

x = 216 cm²

Answer 2

Answer:

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Step-by-step explanation:

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