In the figure given identify the congruent and/or similar triangles and find the value of x and y?

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1 Answer
Mar 17, 2018

See explanation.

Explanation:

From the information about side lengths we can see that all angles are right angled and isosceles. we can say that:

  • #DEF# and #BST# are similar to #DBC# (all 3 triangles have identical angles).

#|EF|=2|DB|#, so the scale of simmilarity is #k=2#

Now we know that: #|DF|=2|DC|#. Since #|DF|+|DC|=3x#, we have: #|DF|=x# and #|CD|=|BD|=2x#

  • #DEF# is congruent to #BST# (corresponding sides are equal)

To calculate #x# we use the Pythagorean theorem for triangle #BCD#

#|BD|^2+|CD|^2=|BC|^2#

#(2x)^2+ (2x)^2=(4sqrt(18))^2#

#4x^2+4x^2=16*18#

#8x^2=16*18#

#x^2=36=> x=6#

Now w euse the Pythagorean theorem for #DEF# to calculate #y#

#6^2+6^2=y^2#

#y^2=72=>y=6sqrt(2)#