Question

The sides of a triangle are in the ratio of 14:18:26 and it's perimeter is 580 CM .Find the area. Also find the altitude corresponding to the smallest side

Answer 1

Step-by-step explanation:

sides of triangle are in ratio of 14:18:26

perimeter of triangle = 580

14x + 18x + 26x = 580

58x = 580

x = 580/58

x = 10

therefore the sides are

14x = 14 × 10 = 140

18x = 18 × 10 = 180

26x = 26 × 10 = 260

area of triangle with sides given we use herons formula

area = √s(s-a)(s-b)(s-c)

s = (a+b+c)/2

where a, b, c are the sides of triangle

$s = \frac{140 + 180 + 260}{2} = \frac{580}{2} = 290 \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{290(290 - 140)(290 - 180)(290 - 260)} \\ = \sqrt{290 \times 150 \times 110 \times 30} \\ = \sqrt{29 \times 5 \times 3 \times 11 \times 3 \times 10000} \\ = 300 \sqrt{29 \times 5 \times 11} \\ \\ = 300 \times 39.93 \\ = 11979 \: sq \: cm$

altitude corresponding to smallest side 140cm

11979 = 1/2 × 140 × h

11979 = 70 × h

h = 11979/70

h = 171 cm

hope you get your answer