Question

The perimeter of a rhombus is 260cm and one of its diagonals is 66cm. Find the area of the rhombus and its other diagonal.

• A. Area $=3696c{m}^2$, BD = 112 cm
• B. Area $=3690c{m}^2$, BD = 112 cm
• C. Area $=3696c{m}^2$, BD = 10 cm
• D. Area $=3690c{m}^2$, BD = 10 cm

Answer 1

The correct option is A

Area $=3696c{m}^2$, BD = 112 cm

Perimeter of rhombus ABCD = 260cm. Diagonal AC = 66cm.

$\therefore$ sides of rhombus $=\frac{260}{4}=65cm.$

In $\Delta ABC$, we have

AB = BC = 65cm and AC = 66cm

$s=\frac{AB+BC+AC}{2}=\frac{65+65+66}{2}=98cm$

$\therefore$ Area of $\Delta ABC$

$=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{98(98-65)(98-65)(98-66)}$

$=\sqrt{98\times 33\times 33\times 32}$

$=\sqrt{49\times 2\times 33\times 33\times 2\times 16}$

$=7\times 2\times 33\times 4=1848c{m}^2$

$\therefore$ Area of rhombus ABCD

$=2\times \text{area of}\Delta ABC=2\times 1848=3696c{m}^2$

Also, area of rhombus $=\frac{1}{2}\times$ Product of its diagonals

$=\frac{1}{2}AC\times BD=\frac{1}{2}\times 66\times BD$

$\Rightarrow BD=\frac{3696\times 2}{66}=112cm$