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An altitude of a triangle is 5/3rd the length of its corresponding base. if the altitude is increased by 8 and base is decreased by 4 the area of triangle would remain same. Find the base and altitude of triangle. Hint(Chapter: linear equation in one veriable)​

Answer» <html><body><p><strong>Answer:</strong></p><p><a href="https://interviewquestions.tuteehub.com/tag/let-11597" style="font-weight:bold;" target="_blank" title="Click to know more about LET">LET</a> the length of <a href="https://interviewquestions.tuteehub.com/tag/corresponding-935567" style="font-weight:bold;" target="_blank" title="Click to know more about CORRESPONDING">CORRESPONDING</a> base be x.</p><p>Thus, altitude will be </p><p>3</p><p>5</p><p> </p><p> x.</p><p></p><p>Now, it is given that altitude is increased by 4 cm i.e., </p><p>3</p><p>5</p><p> </p><p> x+4 and base is decreased by 2 cm i.e., x−2.</p><p></p><p>The area is same for both.</p><p></p><p>Therefore, </p><p>2</p><p>1</p><p> </p><p> ×x× </p><p>3</p><p>5</p><p> </p><p> x= </p><p>2</p><p>1</p><p> </p><p> ×( </p><p>3</p><p>5</p><p> </p><p> x+4)×(x−2)</p><p></p><p>⇒ </p><p>3</p><p>5</p><p> </p><p> x </p><p>2</p><p> = </p><p>3</p><p>5</p><p> </p><p> x </p><p>2</p><p> − </p><p>3</p><p>10</p><p> </p><p> x+4x−8</p><p></p><p>⇒8= </p><p>3</p><p>2</p><p> </p><p> x</p><p></p><p>⇒x=<a href="https://interviewquestions.tuteehub.com/tag/12-269062" style="font-weight:bold;" target="_blank" title="Click to know more about 12">12</a></p><p></p><p>Thus, length of base is 12 cm</p><p></p><p>and length of altitude is </p><p>3</p><p>5</p><p> </p><p> ×12=20 cm.</p></body></html>


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