Maths-
General
Easy

Question


In the figure above, tan B = 3 over 4. If BC = 15 and DA = 4, what is the length of DE ?

The correct answer is: 6


    HINT – Use triangular similarity
    SOLUTION -  It is given that Tan B = 3 over 4
    We know that Tan x =  fraction numerator left parenthesis P e r p e n d i c u l a r space right parenthesis over denominator left parenthesis B a s e space right parenthesis end fraction
 = P over B
    rightwards double arrowP over B =  3 over 4
    rightwards double arrowfraction numerator A C over denominator A B end fraction 3 over 4  rightwards double arrowAC = 3 over 4 AB             ---- (1)
    Using Pythagoras Theorem in triangle ABC
    BC2 = AB2 + AC2
    152 = AB2 +  ( 3 over 4 AB)2
    15= AB2 9 over 16  AB2
    15= 25 over 16 AB2
    15 = 5 over 4 AB
    12 = AB
    It is given that BC =  15 and DA = 4
    Using triangle similarity,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator A C over denominator A B end fraction equals fraction numerator D E over denominator D B end fraction end cell row cell 3 over 4 equals fraction numerator D E over denominator A B minus D A end fraction end cell row cell 3 over 4 equals fraction numerator D E over denominator 12 minus 4 end fraction end cell row cell 3 over 4 equals fraction numerator D E over denominator 8 end fraction end cell end table
    6 = DE
    So, length of DE = 6.

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