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mylen [45]
3 years ago
9

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.
Answer:

A△ABC =

cm2and A△DFG =

cm2.



Pls hellpppppp
Mathematics
1 answer:
Naya [18.7K]3 years ago
4 0

Answer:

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,<u> from The property of similar Triangles</u>

\dfrac{area ABC}{area DFG}=\dfrac{AB^{2} }{DE^{2} }

I.e \dfrac{77+x}{x} = \dfrac{(6 y)^{2} }{(5y)^{2} }

Or, \dfrac{77+x}{x} = \dfrac{36}{25}

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 = \frac{25\times 77}{11}

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

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