Question

One of the diagonals of a rhombus of perimeter 120m is 36m. Find its area and the length of the other diagonal. pls answer fasttt

Answer 1

Answer: $864\ m^2,\ 24\ m$

Step-by-step explanation:

Given

Perimeter of the rhombus is $120\ m$

Length of one of the diagonal is $d_1=36\ m$

All the sides of the rhombus are equal

$\Rightarrow 4a=120\\\Rightarrow a=30\ m$

Area of the rhombus with side and one diagonal is

$\Rightarrow \text{Area=}\dfrac{1}{2}d\sqrt{4a^2-d^2}$

Insert the values

$\Rightarrow \text{Area=}\dfrac{1}{2}\times 36\times \sqrt{4\cdot 30^2-36^2}\\\\\Rightarrow \text{Area= }18\sqrt{3600-1296}\\\Rightarrow \text{Area= }18\times 48\\\Rightarrow \text{Area= }864\ m^2$

Area with two diagonals length can be given by

$\Rightarrow \text{Area =}0.5\times d_1\times d_2 \\\text{Insert the values}\\\Rightarrow 864=36\times d_2\\\Rightarrow d_2=24\ m$

Thus, the area of the rhombus is $864\ m^2$ and the length of the other diagonal is $24\ m$