In the given figure, A,B,C are the mid-points of sides xy, yz and xz respectively of $△ x y z$ .
If AB= 5.5 cm, BC= 3.5 cm and AC= 6 cm, then perimeter of $△ x y z =$ ______ cm.

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Solution

The correct option is C
30

Using mid-point theorem we have,
$B C = \frac{1}{2} Y X \Rightarrow X Y = 2 (B C) = 7 c m$
$A C = \frac{1}{2} Y Z \Rightarrow Y Z = 2 (A C) = 12 c m$
$A B = \frac{1}{2} X Z \Rightarrow X Z = 2 (A B) = 11 c m$
Perimeter of $△ x y z = 7 + 12 + 11$
$= 30 c m$
Hence (c).

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There are two triangles ABC and XYZ such that ΔABC ΔYXZ. their measurement are given as follows: AB =6 cm, AC = 9 cm, BC = 7 cm. Find out the corresponding measurements of triangle YXZ.

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ABC, (see fig. 5.13) X, Y and Z are the mid-points of side AB, side BC and side AC respectively.
AB = 5cm, AC = 9cm and BC = 11cm.
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In the given figure, A,B,C are the mid-points of sides xy, yz and xz respectively of △xyz. If AB= 5.5 cm, BC= 3.5 cm and AC= 6 cm, then perimeter of △xyz= ______ cm.

The correct option is C 30 Using mid-point theorem we have, BC=12YX⇒XY=2(BC)=7cm AC=12YZ⇒YZ=2(AC)=12cm AB=12XZ⇒XZ=2(AB)=11cm Perimeter of △xyz=7+12+11 =30cm Hence (c).

In the given figure, A,B,C are the mid-points of sides xy, yz and xz respectively of $△ x y z$ .
If AB= 5.5 cm, BC= 3.5 cm and AC= 6 cm, then perimeter of $△ x y z =$ ______ cm.

The correct option is C
30

Using mid-point theorem we have,
$B C = \frac{1}{2} Y X \Rightarrow X Y = 2 (B C) = 7 c m$
$A C = \frac{1}{2} Y Z \Rightarrow Y Z = 2 (A C) = 12 c m$
$A B = \frac{1}{2} X Z \Rightarrow X Z = 2 (A B) = 11 c m$
Perimeter of $△ x y z = 7 + 12 + 11$
$= 30 c m$
Hence (c).