Question

The areas of two similar triangles are 25 cm2 and 36cm2 respectively.if the altitude of the first triangle is 2.4cm,find the corresponding altitude of the other

Answer 1

As we know that, for two similar triangles
(Area)₁/(Area)₂ = (side)₁²/(side)₂²

(Area)₁ = 25 cm²
(Area)₂ = 36 cm²
(altitude)₁ = 2.4 cm
(altitude)₂ = x

25/36 = (2.4)²/x²
⇒x² = [(5.76)×36]/25
⇒x = (2.4×6)/5
      =2.88 cm

Answer 2

Answer:

2.88 cm

Step-by-step explanation:

Property : In two similar triangles, the ratio of their areas is the square of the ratio of their sides. and also  In Similar Triangles - ratios of parts, the perimeter, sides, altitudes and medians are all in the same ratio.

Let the altitude of second triangle be x

So,  $\frac{\text{Area of first triangle}}{\text{Area of second triangle}}=\frac{\text{square of Altitude of first triangle}}{\text{Square of Altitude of second triangle}}$

 $\frac{25}{36}=\frac{2.4^2}{x^2}$

 $x^2=\frac{2.4^2 \times 36}{25}$

 $x=\sqrt{\frac{2.4^2 \times 36}{25}}$

 $x=2.88$

Hence the corresponding altitude of the other is 2.88 cm