Question

plz solve the above question

Answer 1

let side of the rhombus be a cm
as all sides of rhombus are equal
therefore perimeter = 4 × side
180 = 4s
s = 45
so the side of the rhombus is 45 cm
let the diagonals be d1 and d2 with d1 = 72cm so ½d1 = 36cm and ½d2 = x
as diagonals are perpendicular bisectors
therefore d1 perpendicular to d2
therefore triangle formed by ½d1, ½d2, side is a right triangle
by Pythagoras theorem,
s² = (½d1)² + (½d2)²
45² = 36² + x²
2025 = 1296 + x²
792 = x²
x = 27
so ½d2 = 27
d2 = 54
area of rhombus = ½(d1*d2)
= ½(36*54)
= 18*54 = 972 cm²

so the other diagonal's length is 54 cm and the area is 972 cm²

Answer 2

this is the best answer