Question

The height corresponding to the longest side of the triangle whose sides are 91 cm,98 cm,105 cm

Answer 1

Using Herons formula
$area = \sqrt{s(s- a)(s - b)(s -c)}$
where a,b,c are sides of Triangle
and s is semi perimeter
$s = \frac{a + b + c}{2}$
Therefore,
$s = \frac{91 + 98 + 105}{2}$
$s = 147$
Now putting values in Herones formula.
$area = \sqrt{147(147 - 91)(147 - 98)(147 - 105)}$
$area = \sqrt{147 \times 56 \times 49 \times 42}$
$area = 4116 \: {cm}^{2}$
Area is also equal to
$\frac{1}{2} \times base \times \: height$
Now height corresponding to the longest height is
$4116 = \frac{1}{2} \times 105 \times height$

$height = 78.4$
Hope it helps!!

Answer 2

78.4 cm is the height of triangle by longest side