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It is given that height to base ratio is 3 : 4 ⇒ Height, h = 3x and Base, b = 4x Area of triangle = <img src="data:image/png;base64,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" class="Wirisformula" alt="1 half cross times b cross times h" width="74" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo»§#215;«/mo»«mi»b«/mi»«mo»§#215;«/mo»«mi»h«/mi»«/math»'/> 864 = <img src="data:image/png;base64,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" class="Wirisformula" alt="1 half cross times 4 x cross times 3 x" width="94" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo»§#215;«/mo»«mn»4«/mn»«mi»x«/mi»«mo»§#215;«/mo»«mn»3«/mn»«mi»x«/mi»«/math»'/> 864  = 6x2 144 = x2 12 = x Height = 3x = 3(12) = 36 units and Base = 4x = 4(12) = 48 units

If the height to base ratio of a triangle ABC is 3:4 and the area is 864 square units. Determine the height and base of this triangle.

Solution for the question - if the height to base ratio of a triangle abc is 3:4 and the area is 864square units. determine the height and base of this triangle