Question

4. The areas of two similar triangles are 25 cm² and 36 cm² respectively. If
the altitude of the first triangle is 3.5 cm then the corresponding altitude
of the other triangle is
(a) 5.6 cm (b) 6.3 cm
(c) 4.2 cm (d) 7 cm​

Answer 1

Given :-

• Areas of two similar triangles are 25 cm² and 36 cm²
• Altitude of the first triangle is 3.5 cm

To find :-

• Corresponding altitude

Solution :-

As we know that

★ The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding altitude.

According to the theorem

→ ar(∆1)/ar(∆2) = (Altitude of ∆1)²/(Altitude of ∆2)²

Let the corresponding altitude be x

→ 25/36 = (3.5/x)²

→ √25/√36 = 3.5/x

→ 5/6 = 3.5/x

→ 5x = 6 × 3.5

→ 5x = 21

→ x = 21/5

→ x = 4.2cm

Hence,

• Corresponding altitude is 4.2cm