Question

triangle ABC is similar to triangle DEF. If ar(triangleABC)= 16/ ar(triangleDEF)= 9 and if AC = 2.4 cm, find the length of side DF.​

Answer 1

✬ DF = 1.8 cm ✬

Step-by-step explanation:

Given:

• ∆ABC and ∆DEF are similar to each other.
• Area of ∆ABC is 16 cm².
• Area of ∆DEF is 9 cm².
• Length of side AC is 2.4 cm.

To Find:

• Length of side DF ?

Solution: Let the length of sides DF be x cm.

As we know that

• The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

➟ ar(∆ABC)/ar(∆DEF) = AC²/DF²

A/q

➟ (AC/DF)² = ar(∆ABC)/ar(∆DEF) = 16/9

➟ (AC/DF)² = 16/9

➟ (AC/DF) = √16/9

➟ 2.4/x = 4/3

➟ 2.4 × 3 = 4 × x

➟ 7.2 = 4x

➟ 7.2/4 = x

➟ 1.8 cm = x

Hence, length of DF is x = 1.8 cm