Mathematics
Grade9
Easy

Question

R and S are midpoints of sides XZ and ZY, respectively, of sides of a triangle ZYX. Find the perimeter of triangle ZYX.

  1. 72
  2. 32
  3. 36
  4. 66

hintHint:

If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.

The correct answer is: 32


    Triangle ZSR is similar to triangle ZYX
    fraction numerator Z R over denominator Z X end fraction equals fraction numerator Z S over denominator Z Y end fraction equals fraction numerator S R over denominator X Y end fraction
space S i n c e space R space a n d space S space a r e space m i d p o i n t s comma
R X equals 11 space a n d space S Y equals space 9 space space space space
X Z equals 11 plus 11 equals 22 space space space space
space Z Y equals 9 plus 9 equals 18 space space space
space X Y equals 32 space
space P e r i m e t e r equals space X Z plus Z Y plus X Y equals 22 plus 18 plus 32 equals 72
    Hence, the correct option is A.

    Perimeter= Sum of all sides.

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