A triangular land having area 336m2 and perimeter 84m has length of an edge 26m.Calculate the measures of remaining sides.
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Answers
Answer:
28cm and 30 cm
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Step-by-step explanation:
The perimeter of a triangle is 84 cm and its area is 336 square cm. If the length of one side of the triangle is 30 cm, then what is the lengths of the remaining two sides of triangle?
Solution: Perimeter of the triangle = 84 cm.
One side = 30 cm.
The sum of the other two sides = 84–30 = 54 cm
Let the other two sides be x cm and (54-x) cm.
By Heron’s formula: 336 = [42*12*(42-x)*(42–54+x)]^0.5
112896 = [42*12*(42-x)*(42–54+x)], or
224 = (42-x)*(x-12) = 42x-x^2–504+12x, or
x^2^ - 54x +728 = 0
x = [54+(2916–2912)^0.5]/2
= [54+2}/2
= 28 cm.
The other two sides are 28 cm and 26 cm. Answer.
Answer:
The perimeter of a triangle is 84 cm and its area is 336 square cm. If the length of one side of the triangle is 30 cm, then what is the lengths of the remaining two sides of triangle?
Solution: Perimeter of the triangle = 84 cm.
One side = 30 cm.
The sum of the other two sides = 84–30 = 54 cm
Let the other two sides be x cm and (54-x) cm.
By Heron’s formula: 336 = [42*12*(42-x)*(42–54+x)]^0.5
112896 = [42*12*(42-x)*(42–54+x)], or
224 = (42-x)*(x-12) = 42x-x^2–504+12x, or
x^2^ - 54x +728 = 0
x = [54+(2916–2912)^0.5]/2
= [54+2}/2
= 28 cm.
The other two sides are 28 cm and 26 cm. Answer.