The length of the perpendicular is 14.69 units.
We have a right - angled triangle with hypotenuse (h) = 21 units, base (b) = 15 units.
We have to find the height of the perpendicular (p) for this right angled triangle.
According to the Pythagoras theorem : for a right angled triangle -
[tex]h^{2} =b^{2} +p^{2}[/tex]
In the question given to us that - h =21 units and b = 15 units. Substituting the values in the above equation, we can the value of p.
[tex](21)^{2}[/tex] = [tex](15)^{2}[/tex] + [tex]p^{2}[/tex]
[tex]p^{2}[/tex] = [tex](21)^{2} -(15)^{2}[/tex]
[tex]p^{2}[/tex] = (21 + 15) x (21 - 15) = 36 x 6 = 216
[tex]p\\[/tex] = 14.69 units
Hence, the length of the perpendicular is 14.69 units.
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