Answer:
CD=14 cm and DE=21 cm
Step-by-step explanation:
Let the rhombus's side be x cm, DN=NF=FM=DM=x xm.
Triangles CDE and FNE are similar, thus,
or
Hence,
and
Since the perimeter of the triangle CDE is 55 cm, we have that
Therefore, CD=14 cm and DE=21 cm
X/y = 4 , x = 4y
x^2 -12y^2 = (4y)^2 - 12y^2 = 16y^2 -12y^2 = 4y^2
The formula of a lateral area of a triangular prism is
LA = (1/2)*(perimeter of a triangle)*h
The perimeter of a triangle is the total of all sides.
Since the length of the base of a triangle is not given yet, use the Pythagorean theorem
base² = 7² + 24<span>²
base</span><span>² = 625
base = 25 cm
The perimeter is 7 + 24 + 25 = 56 cm
Finally the lateral area is
LA = (1/2)*56*30 = 840 cm</span><span>²</span>