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The midpoints of the sides of an equilateral triangle PQR are X, Y and Z if the perimeter of triangle PQR is 24 cm, then what is the perimeter of triangle XYZ?.

The midpoints of the sides of an equilateral triangle PQR are X, Y and Z if the perimeter of triangle PQR is 24 cm, then what is the perimeter of triangle XYZ?. Correct Answer 12 cm

Given
 
 ⇒
 
Here the triangle is an equilateral triangle, hence all sides are equal. 

Formula Used:

Perimeter of equilateral triangle = 3 × side ( Because all sides are equal )

Calculation: 

⇒ 24 = 3 × side 

⇒ Side = 24/3 = 8 cm

⇒ As X , Y , Z are the midpoint of triangle PQR

therefore PR = 8 cm , PZ = 4 cm , ZR = 4 cm , RQ = 8 cm , QY = 4 cm , YR = 4 cm PQ = 8 cm, PX = 4cm, QX = 4cm.

⇒ Using The midpoint theorem “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

Therefore XY = YZ = ZX = 4cm

∴ Perimeter of triangle XYZ = 4 + 4 + 4 = 12 cm

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