Ratio of areas of two triangles with equal height is `2:3`. If base of the smaller triangle is 6 cm, the what is the corresponding base of the bigger triangle?

Explanation

Let the areas of the two triangles be `A_(1)` and `A_(2)`. Let their respective bases be `b_(1)` and `b_(2)`.
`A_(1):A_(2)=2:3` and `b_(1)=6cm`…(Given)
The triangles are of equal heights.
Areas of triangles with equal heights are proportional to their corresponding bases.
`:.(A_(1))/(A_(2))=(b_(1))/(b_(2)):.2/3=6/(b_(2)):.b_(2)=(6xx3)/2`
`:.b_(2)=9cm`
The corresponding base of the bigger triangle is 9cm.