Question

the peremeter of the rhombus is 20 cm. one of it diagnal is 8 cm. find the area of rhombus and length of other diagnal .

please it is very urgent

Answer 1

$\huge\mathfrak{\underline{\underline{Question:-}}}$

The perimeter of the rhombus is 20 cm. one of it diagnal is 8 cm. find the area of rhombus and length of other diagnal .

$\huge\mathfrak{\underline{\underline{Given:-}}}$

• Perimeter of rhombus = 20 cm.
• Diagonal of rhombus = 8 cm.

$\huge\mathfrak{\underline{\underline{Concept \:used:-}}}$

• Perimeter of rhombus = 4 × sides
• We know that the diagonal of rhombus bisect each other at right angle. (90°).

$\huge\mathfrak{\underline{\underline{Solution:-}}}$

Side of the rhombus = 4 × sides

Hence, side = $\frac{20}{4}$ = 5cm.

We know that diagonal length is 8 cm.

Half of the length is $\frac{8}{2}$ = 4cm.

$(\frac{d}{2})^{2} + ( \frac{d1}{2} )^{2} = {5}^{2} \\ = > {4}^{2} + ( \frac{d1}{2} )^{2} = {5}^{2} \\ = > ( \frac{d1}{3} )^{2} = 9 \\ = > \frac{d1}{2} = 3 \\ = > d1 = 3 \times 2 \\ = > d1 = 6$

Area:-

$\frac{1}{2} \times d1 \times d \: = \frac{1}{2} \times 8 \times 6 = {24cm}^{2}$

$\huge\mathfrak{\underline{\underline{Answer:-}}}$

The area of rhombus is 24 cm².

Answer 2

$\huge \red{ \underline{ \mathtt{Your \ Answer:}}}$

24 cm²