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

The Area of Δ DFG is 175 cm²

The Area of Δ ABC is 252 cm²

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

`(area ABC)/(area DFG)`=
`(AB^(2) )/(DE^(2) )`

I.e
`(77+x)/(x)` =
`((6 y)^(2) )/((5y)^(2) )`

Or,
`(77+x)/(x)` =
`(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 =
`(25* 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