Question

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

Answer 1

Answer:

Step-by-step explanation: 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=  

2

a+b+c

​  

=  

2

13+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=  14 /84

​  

=6cm

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