SOLUTION: An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to t

Question 1022222: An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?
A) 18.8 cm
B) 24.2 cm
C) 42.0 cm
D) 72.7 cm
Found 2 solutions by FrankM, MathTherapy:
Answer by FrankM(1040) (Show Source): You can put this solution on YOUR website!
The longest side, 2X must be less than the sum of the 2 shorter sides, X+21

C
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?
A) 18.8 cm
B) 24.2 cm
C) 42.0 cm
D) 72.7 cm

Since 21 is one of the shorter sides, it follows that 2x MUST be the longest side
We then get: 2x < x + 21
2x - x < 21
x < 21
Therefore, the longest side, or 2x < 42
Since the longest side, or 2x < 42, then the longest side's length can either be 18.8 cm (choice A), or 24.2 cm (choice B),
but since one of the shorter sides is 21, the
RELATED QUESTIONS
The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the... (answered by vleith)
The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by josgarithmetic)
The sum of the lengths of any two sides of a triangle must be greater than the third... (answered by stanbon,MathTherapy)
An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation (answered by solver91311)
The perimeter of a triangle is 122 cm. If the lengths of the sides of the triangle are (answered by ewatrrr)
Give the measure of the base of an isosceles triangle whose perimeter is 60 cm and one of (answered by ikleyn)
Triangle ABC is an acute triangle. Two of it sides measure 11 cm and 14 cm. What is the... (answered by MathLover1)
If a triangle has side lengths of 5 cm, 8 cm, and 10 cm, what type of triangle is it? (answered by Alan3354)
the hypotenuse of a right triangle is 65 cm. one side is 10 cm shorter than twice the... (answered by nerdybill)