Question

Perimeter of a rhombus is 42 and one of the diagonals is 12 cm find its area

Answer 1

Step-by-step explanation:

first write what is given then write the area of rhombus then solve as I solved above

Answer 2

$\large\bf\underline{Given:-}$

• perimeter of rhombus = 42 unit's
• Length of one diagonal = 12cm.

$\large\bf\underline {To \: find:-}$

• Area of rhombus.

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

$\bf \dag \: perimeter \: of \: rhombus = 2 \times \sqrt{d_1 {}^{2} +d_2 {}^{2} }$

• Let the other diagonal be x units.

Perimeter of rhombus = 42 units.

$\dashrightarrow \rm \: 2 \times \sqrt{12 {}^{2} + {x}^{2} } = 42 \\ \\ \dashrightarrow \rm \: \sqrt{144 + {x}^{2} } = \cancel \frac{42}{2} \\ \\ \dashrightarrow \rm \: \sqrt{44 + {x}^{2} } = 21 \\ \\ \dashrightarrow \rm \: 44 + {x}^{2} = {21}^{2} \\ \\ \dashrightarrow \rm \: 44 + {x}^{2} = 441 \\ \\ \dashrightarrow \rm \: {x}^{2} = 441 - 44 \\ \\ \dashrightarrow \rm \: {x}^{2} = 397 \\ \\ \dashrightarrow \rm \: x = \sqrt{397}$

So the other diagonal = √397

$\bf \dag \: area \: of \: rhombus = \frac{1}{2} \times \: d_1 \times d_2$

$\longmapsto \rm \:ar. \: of \: rhomnus = \frac{1}{2} \times 12 \times \sqrt{397} \\ \\ \longmapsto \rm \:ar. \: of \: rhomnus = 6 \times \sqrt{397} \\ \\ \longmapsto \rm \:ar. \: of \: rhomnus = 119.54 \: sq.units$