LET sides be \[a-d,a,a+d\]and as it is a right ANGLED TRIANGLE \[{{(a-d)}^{2}}+{{a}^{2}}={{\left( a+d \right)}^{2}}\] Þ \[{{a}^{2}}+{{d}^{2}}-2ad+{{a}^{2}}={{a}^{2}}+{{d}^{2}}+2ad\] Þ \[a=4d\Rightarrow d=\frac{a}{4}\]. Hence the sides are \[\frac{3A}{4},a,\frac{5a}{4}\] i.e., in ratio 3 : 4 : 5. "> LET sides be \[a-d,a,a+d\]and as it is a right ANGLED TRIANGLE \[{{(a-d)}^{2}}+{{a}^{2}}={{\left( a+d \right)}^{2}}\] Þ \[{{a}^{2}}+{{d}^{2}}-2ad+{{a}^{2}}={{a}^{2}}+{{d}^{2}}+2ad\] Þ \[a=4d\Rightarrow d=\frac{a}{4}\]. Hence the sides are \[\frac{3A}{4},a,\frac{5a}{4}\] i.e., in ratio 3 : 4 : 5. ">
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If the sides of a right angled triangle be in A. P. , then their ratio will be

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) 10 months ago

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LET sides be \[a-d,a,a+d\]and as it is a right ANGLED TRIANGLE \[{{(a-d)}^{2}}+{{a}^{2}}={{\left( a+d \right)}^{2}}\] Þ \[{{a}^{2}}+{{d}^{2}}-2ad+{{a}^{2}}={{a}^{2}}+{{d}^{2}}+2ad\] Þ \[a=4d\Rightarrow d=\frac{a}{4}\]. Hence the sides are \[\frac{3A}{4},a,\frac{5a}{4}\] i.e., in ratio 3 : 4 : 5.
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