Step-by-step explanation:
kartik2507
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
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Verified answer
Step-by-step explanation:
kartik2507
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
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