Two sides of a triangle have lengths 10 and 15 what must be true about the length of the third side

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Consider the triangle. A triangle has angle measures of 45 degrees, 45 degrees, and 90 degrees. Which statement is true about the lengths of the sides? Each side has a different length. Two sides have the same length, which is less than the length of the third side. The three sides have the same length. The sum of the lengths of two sides is equal to the length of the third side.

Two sides of a triangle have lengths

Solution 1 (Process of Elimination)

The shortest side length has the longest altitude perpendicular to it. The average of the two altitudes given will be between the lengths of the two altitudes, therefore the length of the side perpendicular to that altitude will be between

Solution 2

Let the height to the side of length

Because the area of a triangle is

Solution 3 (Answer Choices)

Let be the height of triangle when the base is

Video Solution

https://youtu.be/27TpizTnMeM

~savannahsolver

See Also

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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