Question

find its length and longest side.

Answer 1

Find the area:

SemiPerimeter = ( 35 + 54 + 61) ÷ 2 = 75

Area = √p(p - a)(p - b)(p - c)

Area = √75 (75 - 35)(75 - 54)(75 - 61) = 939.15 cm²

Find the longest altitude:

Area = 1/2 x base x height

939.15 = 1/2 x 35 x height

height = 53.67 cm

Answer: The longest altitude is 53.67 cm

Answer 2

Given

Sides of a triangle are 35 cm , 54 cm and 61 cm .

Half perimeter = 35 + 54 + 61 = 150/2 = 75.

Area = √s(s-a) (s-b) (s-c)

= √75 (75-35) (75-54) (75-61)

= √75 (40) (21) (14)

= √882000

${939cm}^{2}$

finding the height --

Area of triangle =

$\frac{1}{2} \times base \times height$

putting the values --

939 = 1/2 x 35 x height

939 = 17.5 x height

height = 939/17.5

height = 53.65 cm .

$\bold{Answer \: = \: The \: longest \: altitude \: is \: 53.65cm}$