Question

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

Answer 1

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, from The property of similar Triangles

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

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