Question

The sides of a triangle are 26 cm, 28 cm and 30 cm. Its area is equal to the area of a parallelogram whose base is 28 cm. The height of parallelogram is ______.

Options

• 8 cm

• 12 cm

• 15 cm

• 30 cm

Answer 1

The sides of a triangle are 26 cm, 28 cm and 30 cm. Its area is equal to the area of a parallelogram whose base is 28 cm. The height of parallelogram is 12 cm.

Explanation:

Semi-perimeter s = `(26 + 28 + 30)/2` = 42.

Triangle area by Heron:

`sqrt(s(s - 26)(s - 28)(s - 30))` 

= `sqrt(42 xx 16 xx 14 xx 12)` 

= 336 cm²

Parallelogram area

= Base × Height

So, Height = `"Area"/"Base"`

= `336/28`

= 12 cm