Answer: [tex]864\ m^2,\ 24\ m[/tex]
Step-by-step explanation:
Given
Perimeter of the rhombus is [tex]120\ m[/tex]
Length of one of the diagonal is [tex]d_1=36\ m[/tex]
All the sides of the rhombus are equal
[tex]\Rightarrow 4a=120\\\Rightarrow a=30\ m[/tex]
Area of the rhombus with side and one diagonal is
[tex]\Rightarrow \text{Area=}\dfrac{1}{2}d\sqrt{4a^2-d^2}[/tex]
Insert the values
[tex]\Rightarrow \text{Area=}\dfrac{1}{2}\times 36\times \sqrt{4\cdot 30^2-36^2}\\\\\Rightarrow \text{Area= }18\sqrt{3600-1296}\\\Rightarrow \text{Area= }18\times 48\\\Rightarrow \text{Area= }864\ m^2[/tex]
Area with two diagonals length can be given by
[tex]\Rightarrow \text{Area =}0.5\times d_1\times d_2 \\\text{Insert the values}\\\Rightarrow 864=36\times d_2\\\Rightarrow d_2=24\ m[/tex]
Thus, the area of the rhombus is [tex]864\ m^2[/tex] and the length of the other diagonal is [tex]24\ m[/tex]
