Question

the areas of two similar triangles are 81 and 49 respectively.if the altitute of the bigger triangle is 4.5cm,then find the corresponding altitute of the smaller triangle.

Answer 1

area ΔABC = 1/2 * base * height

In similar triangles, base1 / base2 = height1 / height2 = side1/ side2  (of the three corresponding sides).

Also   Area1 / Area2  = (altitude1 / altitude2 )^2

Ratio of altitudes = square root( 81/49) = 9/7  > 1

Altitude of smaller triangle =  4.5 / (9/7) = 3.5 cm

Answer 2

Altitude of the smaller triangle=3.5