In a rhombus with diagonals of 10 and 14 cm, the midpoints of the sides are sequentially connected by segments.
In a rhombus with diagonals of 10 and 14 cm, the midpoints of the sides are sequentially connected by segments. Determine the type of the quadrangle and find its perimeter
Each of the diagonals of the rhombus divides it into two equal isosceles triangles.
∆ABS = ∆ADС;
∆АВD = ∆СВD.
Consider the triangle ∆ABС. KM is its middle line, which is equal to half of its base:
KM = AC / 2;
KM = 10/2 = 5 cm.
NT = KM = 5 cm.
Consider a triangle ∆ABD. НK is its middle line. It is equal to half the base of BD:
НK = BD / 2;
НK = 14/2 = 7 cm.
MT = НK = 7 cm.
The perimeter of this quadrangle is equal to the sum of the lengths of the segments MT, НK, NT and KM:
P = MT + НK + НT + KM;
P = 5 + 5 + 7 + 7 = 24 cm.
Answer: This quadrilateral is a rectangle with a perimeter of 24 cm.