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Two sides of a triangle are 5 cm and 12 cm long. The measure of third sides is an integer in cm. if the tirangles is an obtuse tirangle, then how many such triangles are possible ?A. 9B. 8C. 7D. 6 |
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Answer» Correct Answer - D Two sides of a triangle 5 cm and 12 cm. Let `a=5 cm and b=12 cm` Let the third side be x cm `therefore 12-5 lt x lt 12 +5` `rArr7 lt xlt 17` `therefore` Possible integer values for x are 8,9,10,11,12, 13,14,15,and 16. Case 1: If b is the following side then `b^2gt a^2+x^2 ` `rArr 12^2gt 5^2+x^2` `rArr 144=25gt x^2` `rArr x^2lt 119` `therefore x` can be , 8,9 or 10. Case 2: IF x is the longest side, then `x^2gt a^2+b^2` `rArr x^2gt 5^2+12^2rArrx^2rArr169` `therefore x` can be `14,15 or 16` `therefore` Number of possible triangles. `=6 (because "The measurements third side is an integer is cm")`. |
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