The lengths of the diagonals of a rhombus are 18 cm and 24 cm. What is its perimeter and what is the distance between the parall
el sides?
I don't know the distance but the perimeter is 60cm
I don't know the distance but the perimeter is 60cm
2 answers:
Answer:
Perimeter = 60 cm
Distance between the parallel sides = 14.4 cm
Step-by-step explanation:
In the given rhombus ABCD, AC = 24 cm and BD = 18 cm
As we know in a rhombus BC² = OB² + OC²
BC² = (18/2)²+ (24/2)² = 9² + 12² = 81 + 144 = 225
BC = √225 = 15 cm.
So perimeter of the rhombus = 4×15 = 60 cm
Area of rhombus = (1/2)×Multiplication of diagonals = (1/2)×18×24 = 216 cm²
And from the given diagram area of rhombus ABCD = 2×area of ΔABD
= 2×(1/2)×BC×BE = BC×BE = 15×BE
Since area of rhombus is 216 cm², therefore
15×BE = 216
BE = 216/15 = 14.40 cm
Therefore the distance between two parallel lines is 14.40 cm.
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Hope this helps!