Question

A triangle has side 35cm 54cm and 61cm long find its area also find the smallest of its altitudes solve class 9

Answer 1

Step-by-step explanation:

we use herons formula to find the area

sides are a = 35, b = 54, c = 61

s = (a+b+c)/2

s = (35+54+61)/2

s = 150/2

s = 75

herons formula

$= \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\ = \sqrt{75 \times 40 \times 21 \times 14} \\ = \sqrt{3 \times 5 \times 5 \times 2 \times 2 \times 2 \times 5 \times 3 \times 7 \times 2 \times 7} \\ = 3 \times 5 \times 2 \times 2 \times 7 \times \sqrt{5} \\ = 420 \sqrt{5}$

area of triangle = 420√5 sq cm

area of triangle =

$\frac{1}{2} \times b \times h = 420 \sqrt{5} \\ \frac{1}{2} \times 61 \times h = 420 \sqrt{5} \\ h = \frac{420 \sqrt{5} \times 2}{61} \\ h = 30.79cm$

longest base will have a shorter altitude

hope you get your answer