Question

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

Answer 1

Hi ,

Let A1 and A2 are areas of two

Triangles and H and h are their

corresponding altitudes .

A1 = 25 cm²

A2 = 36 cm²

H = 2.4 cm, h = ?

h²/H² = A2/A1

h²/( 2.4 )² = 36/25

h² = ( 36 × 2.4 × 2.4 )/25

h = ( 6 × 2.4 )/5

h = 2.88 cm

I hope this helps you.

: )

Answer 2

Let the altitude of second triangle be X cm.

Area of first triangle = 25 cm

And,

Area of second triangle = 36 cm.

Altitude of first triangle = 2.4 cm.



Let Altitude of second triangle = Xcm



As we know that the area's of two similar triangles are in the ratio of the squares of corresponding Altitudes.



So,

Area of first triangle / Area of second triangle = (Altitude of first triangle / Altitude of second triangle)² .



Area of first triangle / Area of second triangle = (Altitude of first triangle)² / ( Altitude of second triangle)².

25/24 = (2.4)² / X²

X = 2.88 cm

Hence,

Altitude of second triangle = X = 2.88 cm.