Question

The perimeter of a rhombus is 180 cm and one of its diagonals is 72 cm. Find the length
of the other diagonal and the area of the rhombus.
​

Answer 1

$\huge\mathbb{\underline{\underline{\purple{SOLUTION:-}}}}$

Given:-

The perimeter if rhombus 180cm

one diagonal of rhombus 72cm

To find:-

The length of other diagonal

the area of rhombus

$\sf\underline{\underline{\red{According\:to\: question:-}}}$

• Find the side of rhombus
• we know that the perimeter of rhombus is 4×side

Then :-

$\sf\implies 4\times sides=180\\ \\ \sf\implies side=\frac{180}{4}\\ \\ \sf\implies side=45cm$

The side of rhombus is 45cm

Then d1=72cm

d2=d2

Then by the pyrhagras theorm

in figure which is in attachment:-

$\sf AC{}^{2}=AB{}^{2}+BC{}^{2}$

Then the d2 :-

$\sf (\frac{d1}{2}){}^{2}+(\frac{d2}{2}){}^{2}=side {}^{2}\\ \\ \sf\leadsto (\frac{72}{2}){}^{2}+(\frac{d2}{2}){}^{2}=45{}^{2}\\ \\ \sf\leadsto \frac{5184}{4}+\frac{d2{}^{2}}{4}=2025\\ \\ \sf\leadsto 1296+\frac{d2{}^{2}}{4}=2025\\ \\ \sf\leadsto \frac{d2{}^{2}}{4}=2025-1296\\ \\ \sf\leadsto \frac{d2{}^{2}}{4}=729\\ \\ \sf\leadsto d2{}^{2}=729×4\\ \\ \sf\implies d2{}^{2}=2916\\ \\ \sf\implies d2=\sqrt{2916}\\ \\ \sf\leadsto d2=54cm$

D2=54cm

The other diagonal is 54 cm

Now find the area of rhombus:-

$\sf Area\:of\: Rhombus =\frac{1}{2}\times product\:of\: diagonals$

Diagonals =54cm and 72cm

$\sf\leadsto Area\:of\: rhombus=\frac{1}{2}\times 54cm\times 72cm\\ \\ \sf\leadsto Area=\frac{\cancel3888}{\cancel2}\\ \\ \sf\implies Area\:of\: rhombus=1944cm{}^{2}$

$\boxed{\underline{\red{Other\: diagonal=54cm}}}$

$\boxed{\underline{\red{Area=1944cm{}^{2}}}}$

#BAL

#Answewithquality