Question

Express the ratio of the area of triangle abc to the area of triangle edc

Answer 1

The area of triangle ABC is 30.9990 square units.

The image shows a triangle (ABC) with side lengths AB = 20, AC = 8, and BC = 13. We are asked to find the area of triangle ABC.

The semi-perimeter (s) as mentioned before: s = (20 + 8 + 13) / 2 ≈ 20.5

Substitute s and the side lengths into Heron's formula:

Area ≈ √(20.5 * (20.5 - 20) * (20.5 - 8) * (20.5 - 13))

Evaluate the expression using your calculator. Rounding to four decimal places, you get:

Area ≈ √(20.5 * 0.5 * 12.5 * 7.5)

≈ √(978.75)

≈ 30.9990

Answer 2

Given :

Two similar triangle.

To Find :

The ratio of the area of triangle abc to the area of triangle edc.

Solution :

ΔABC ~ ΔAPQ (AA criterion for similar triangles)

Since both the triangles are similar, using the theorem for areas of similar triangles we have :

`(Area \ of \ \Delta ABC)/(Area \ of \ \Delta EDC) = (AC)/(EC)\\\\(Area \ of \ \Delta ABC)/(Area \ of \ \Delta EDC) = (20+8)/(20)\\\\(Area \ of \ \Delta ABC)/(Area \ of \ \Delta EDC) = 1.4`

Therefore, ratio of area of triangle is 1.4 .