The triangles abc and dfg are similar and the ratio of their corresponding sides is 6: 5. the area of the triangle abc is greater than the area of the triangle dfg by 77 cm2. find the areas of these triangles.

a△abc =
cm2and a△dfg =
cm2.

The Area of Δ DFG is 175 cm²

The Area of Δ ABC is 252 cm²

Step-by-step explanation:

Given as :

The Δ ABC is similar to the Δ DFG

The area of the triangle ABC is greater than the area of the triangle DFG by 77 cm²

Let The area of  Δ DFG = x cm²

So, The area of  Δ ABC = ( 77 + x ) cm²

The ratio of corresponding sides of  Δ ABC and  Δ DEF = 6 : 5

Let The side AB = 6 y

And The side DE = 5 y

Now, from The property of similar Triangles

=

I.e =

Or, =

Or, 25 × (77 + x ) = 36 x

Or,  25 × 77 + 25 x = 36 x

Or,  25 × 77 = 36 x - 25 x

Or, 11 x =  25 × 77

∴  x =

I.e x = 175 cm²

So,The Area of Δ DFG = x  = 175 cm²

And The Area of Δ ABC = x + 77  = 175 + 77  = 252 cm²

Hence, The Area of Δ DFG is 175 cm²

And The Area of Δ ABC is 252 cm²    Answer

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1