Consider four triangles having sides $(5, 12, 9), (5, 12, 11), (5, 12, 13)$ and $(5, 12, 15)$ . among these, the triangle having maximum area has sides.

(5, 12, 9)

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(5, 12, 11)

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(5, 12, 13)

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(5, 12, 15)

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Solution

The correct option is C $(5, 12, 13)$
Area of a triangle is given by $\frac{1}{2} h \times b$ , where $h$ is the height of the triangle and $b$ is base of the triangle.
Let the base of the triangle is $5$ , which is fixed. therefore if the height of the triangle is maximum then it's area will be maximum.
Height is maximum when a triangle is a right angle triangle.
Thus, triangle having sides $(5, 12, 13)$ has maximum area.

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Consider four triangles having sides (5,12,9),(5,12,11),(5,12,13) and (5,12,15). among these, the triangle having maximum area has sides.

Consider four triangles having sides $(5, 12, 9), (5, 12, 11), (5, 12, 13)$ and $(5, 12, 15)$ . among these, the triangle having maximum area has sides.