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

Question

OLga [1]

3 years ago

6

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.

Mathematics

2 answers:

aev [14] · Answer 1 · 2022-02-09T02:15:37+03:00

aev [14]3 years ago

5 0

Answer:

Step-by-step explanation:

Elden [556K] · Answer 2 · 2022-02-09T03:24:29+03:00

Answer:

Area of triangle DFG = 175

Area of triangle ABC = 252

Step-by-step explanation:

It is given that,

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.

Let area of triangle DFG = x then area of triangle ABC = x + 77

<u>To find the area of 2 triangles</u>

ar(DFG)/ar(ABC = (5/6)²

x/(x + 77) = 25/36

36x = 25x + (25 * 77)

36x - 25x = 25 * 77

11x = 25 * 77

x = 175

Therefore area of triangle DFG = 175

Area of triangle ABC = 175 + 77 = 252