A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Explanation

Let ABC be a triangle with sides
AB = 26 cm, BC = 28 cm, CA = 30 cm
Now, `s=(AB+BC+CA)/(2)`
`=((26+28+30)/(2)) cm`
`rArr s=(84)/(2) cm`
`rArr s=42 cm`
Area of `DeltaABC=sqrt(42(42-26)(42-28)(42-30))`
`=sqrt(42xx16xx14xx12)` `" "` (by Heron's formula)
` = sqrt(7xx2xx3xx2xx2xx2xx2xx7xx2xx3xx2xx2)`
`=7xx2xx2xx2xx2xx3`
`=336 cm^(2)`
We know that, area of parallelogram = base `xx` height `" "` ...(1)
We have, area of parallelogram = area of `DeltaABC " " `(given)
`=336 cm^(2)`
From eq. (1), we have
base `xx` height = 336
`rArr 28xx` height = 336
`rArr "height" = (336)/(28)`
`rArr "height" = 12 cm`