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in a triangle the bis sector and median
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are perpendicular and both equal to 12
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find the sides of the triangle and its
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area to assess the difficulty press
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pause and try to solve this relatively
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complex problem there are different ways
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to solve it but let's go through the
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simplest method the right triangles a o
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and d o are congruent by a leg and an
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acute angle from the congruence of the
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triangles follows the equality of their
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corresponding sides so AO will equal o d
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and equal to half of a d also AB equals
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BD which by the condition is equal to DC
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meaning each segment will be half of BC
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by the property of the bis sector the
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ratio of AE to e c will equal the ratio
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of ab to BC and considering that AB is
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half of BC we get one2 let's denote AE
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as X then EC will be twice as much or 2
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x now comes the most important moment in
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solving the problem it turns out that if
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we draw or extend something further the
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rest of the solution will be Elementary
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this is the case where one additional
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line determines the solution of the
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problem so we need to draw the midline
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of triangle BCE labeling it DK by
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construction Point K divides segment EC
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in half so EK equal KC and equals x
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moreover by the property of the midline
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DK will be parallel to be and equal to
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half of it now notice that OE is the
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midline of triangle a DK so it will
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equal half of DK but then it will equal
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the difference between be and Oe from
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the right triangle AB we find side AB
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and then find side BC which is twice as
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long as AB from the right triangle AE
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using the Pythagorean theorem we find X
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and this gives us the values for the
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triangle to find the area of triangle AB
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we use the median of triangle b d which
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divides triangle BC into two equal
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triangles as a result we find that the
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area of triangle AB equals the area of
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triangle bde and equals the area of
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triangle dce we calculate this area as
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half the product of the base and the
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height thus the area of triangle ABC
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will be three times greater the answer
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is side A B = 3 * the < TK of 13 side BC
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is 6 * the < TK of 13 and side a = 9 *
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theare < TK of 5 the area of the
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triangle equals 108 square units the
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problem is solved if you find the video
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interesting leave a like And subscribe
