Question

The area of a rhombus is 1080 sq. m and one of its diagonal is 72 m.What is the perimeter of the rhombus?​

Answer 1

$\huge\bold{ANSWER~:}$$<b><i>$

➣ We know that area of rhombus :-

$= \frac{1}{2} \times two \: diagonals$

➣ Here we have one diagonal 72 we have to first find 2nd diagonal.

$1080 = \frac{1}{2} \times 72 \times ac\\ \\ \frac{1080 \times 2}{72} = ac \\ \\ ac = 30 \: m$

➣ We know that diagonal of rhombus bisect perpendicular each other.

➣ Now in ΔOAD

${AD}^{2}={OD}^{2} +{OA}^{2}$

$= \sqrt{ {36}^{2} + {15}^{2} } \\ \\ = \sqrt{1521} = 39 \: m$

➣ We know that rhombus have four sides equal.

$Perimeter=4* AD$

$= 4 \times 39 \\ \\ = 156 \: m$

${\large\bold\color{Red}{Answer~is~156~m~. }}$

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