Question

If triangle ABC similar to triangle DEF. Such that AB= 5 cm. Area of triangle = 20 cm square and area of triangle = 45 cm square. Determine DE.find answer

Answer 1

The length of DE is 15/2 cm.

Explanation:

To determine the length of DE, we can use the fact that the areas of similar triangles are proportional to the squares of their corresponding side lengths.

Given that triangle ABC is similar to triangle DEF, we can set up the proportion:

(AB/DE)^2 = (Area of triangle ABC/Area of triangle DEF)

Plugging in the given values, we have:

(5/DE)^2 = 20/45

Simplifying the equation:

(5/DE)^2 = 4/9

Cross-multiplying:

5^2 = (DE)^2 * (4/9)

25 = (DE)^2 * (4/9)

To solve for DE, we can isolate (DE)^2:

(DE)^2 = 25 * (9/4)

(DE)^2 = 225/4

Taking the square root of both sides:

DE = √(225/4)

DE = 15/2

Therefore, the length of DE is 15/2 cm.