Question

If the sides of a triangle are 11cm,15cm,16cm then the attitude to the longest side is ?

Answer 1

Find the semi-perimeter:

p = ( 11 + 15 + 16 ) ÷ 2 = 21

Find the area:

Area = √p(p-a)(p-b)(p-c)

Area = √21(21 - 11)(21 - 15)(21 - 16)

Area = √6300

Area = 30√7 cm²

Find the altitude of the longest side:

Area = 1/2 x base x height

30√7 = 1/2 x 16 x height

30√7 = 8 x height

height =  30√7  ÷ 8 = (15√7)/4 or  9.92 cm

Answer: The altitude of the longest side is 9.92 cm