The length of the side m are obtained using the theorem of Pythagoras and proportional triangles to give;
a) m ≈ 28.4
b) m ≈ 12.09
c) m ≈ 9.38
a) The given triangle, is a right triangle.
The length of the legs of the triangle are; 33 and 56.
According to Pythagorean theorem, the length of the hypotenuse side, l, is therefore;
l = √(33² + 56²) = 65
From the formula for the area of a triangle, we have;
Area of a triangle, A, equals half the base length multiplied by the height.
A = 0.5 × Base length × Height
For the right triangle, we have;
A = 0.5 × Leg 1 × Leg 2
Which gives;
A = 0.5 × 33 × 56 = 924
However;
A = 0.5 × l × m
Where;
l = The hypotenuse = The base length = 65
m = The height of the triangle
Which gives;
A = 0.5 × 65 × m = 924
m = 924/(0.5 × 65) ≈ 28.4
b) The side m is parallel the 14 units long side.
The proportion the side m divides a side of the triangle = 3 and 19
Given that the triangle formed by m is proportional to the larger triangle, we have;
m/14 = 19/(19+3)
c) From the proportionality of similar triangles, we have;
m/16 = 17/(14+15)
Learn more about the proportionality of similar triangles here:
https://brainly.com/question/21874065
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