Question

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13cm, 14cm and 15cm and the parallelogram stands on the base 14cm , find the height of the parallelogram. ​

Answer 1

Answer:

Given sides of the triangle are 13cm,14cm,15cm

We know that the area of the triangle is s(s−a)(s−b)(s−c)

where a,b,c are the sides of the triangle and

s=2a+b+c=213+14+15=21

Therefore, the area of the triangle is 21(21−13)(21−14)(21−15)=7056=84 -------(1)

Given that base of the parallelogram is 14cm

Given that the triangle and the parallelogram have the same area.

Therefore, area of parallelogram = area of triangle

⟹base * height = area of triangle

⟹14 * height = area of triangle

⟹14 * height = 84  (from (1))

⟹height=1484=6cm