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Answers
We solve this using Pythagoras.
We know that all 4 sides of a rhombus are equal.
So perimeter of rhombus = 4s
180 = 4s
s = 180/4
s = 45
Now, we can see that the diagonals of a rhombus split it into 4 right triangles.
We're given the length of one of the diagonals = 72 cm.
So we take half of it as one of the sides of a triangle = 72/2 = 36
Now, we have two sides of a right triangle, so we can find the third using pythagoras.
45^2 = 36^2 + x^2
x^2 = 45^2 - 36^2
x^2 = 729
x = √729
x = 27
So, the third side = 27
This third side is also half of the second diagonal, so the diagonal = 2x = 2*27 = 54
Now, for part 2 we have to find area of the rhombus.
Area of rhombus = (Diagonal * Diagonal)/2
= (72*54)/2
= 3888/2
= 1944u²
Hope this Helped!
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