Question

Ratio of area of 2 similar triangles are 2:3. Area of the larger triangle is 90cm sq. Finf the area of the smaller triangle

Answer 1

Answer:

40 cm^2

Step-by-step explanation:

Let say side on smaller triangle =  2a , 2b , 2c

 side of larger triangle = 3a , 3b , 3c

Area of small Triangle = √(s(s-2a)(s-2b)(s-2c)  while s = (2a+2b+2c)/2

= √(a+b+c)(b+c-a)(a+c-b)(a+b-c)  

 Area of larger triangle = √(s(s-3a)(s-3b)(s-3c)  while s = (3a+3b+3c)/2

 = √(3/2)(a+b+c)(3/2)(b+c-a)(3/2)(a+c-b)(3/2)(a+b-c)

= (3/2)(3/2)√(a+b+c)(b+c-a)(a+c-b)(a+b-c)

= (9/4)* (area of smaller triangle)

(9/4)* (area of smaller triangle) = 90 cm^2

Area of smaller triangle = 40 cm^2

Answer 2

$\Large\text{Answer:}$

Let say side on smaller triangle =  2a , 2b , 2c

 side of larger triangle = 3a , 3b , 3c

Area of small Triangle = √(s(s-2a)(s-2b)(s-2c)  while s = (2a+2b+2c)/2

= √(a+b+c)(b+c-a)(a+c-b)(a+b-c)  

 Area of larger triangle = √(s(s-3a)(s-3b)(s-3c)  while s = (3a+3b+3c)/2

 = √(3/2)(a+b+c)(3/2)(b+c-a)(3/2)(a+c-b)(3/2)(a+b-c)

= (3/2)(3/2)√(a+b+c)(b+c-a)(a+c-b)(a+b-c)

= (9/4)* (area of smaller triangle)

(9/4)* (area of smaller triangle) = 90 cm^2

Area of smaller triangle = 40 cm^2