Question

The diagonals of a rhombus are in the ratio 3 : 4. If the longer diagonal is 12 cm, then find the area of
the rhombus​

Answer 1

$\huge{\boxed{\mathtt{\purple{Answer}}}}$

Let diagonals of arhombusABCD are AC=3k and BD=4k cm.which meet at point O.

Perimeter=4×side

40/4=side

10 cm.=side=AB=BC=CD=DA.

In right angled triangle AOB

OA^2+OB^2=AB^2

(AC/2)^2+(BD)^2=(10)^2

9k^2/4+4k^2=100

(25k^2)/4=100

k^2=16

0k=+/-4

AC=3k=3×4=12cm.

BD=4k=4×4=16cm.

each side =10 cm. ,

Answer 2

Answer:

$\huge{\boxed{\mathtt{\purple{Answer}}}}Answer</p><p></p><p>Let diagonals of arhombusABCD are AC=3k and BD=4k cm.which meet at point O.</p><p></p><p>Perimeter=4×side</p><p></p><p>40/4=side</p><p></p><p>10 cm.=side=AB=BC=CD=DA.</p><p></p><p>In right angled triangle AOB</p><p></p><p>OA^2+OB^2=AB^2</p><p></p><p>(AC/2)^2+(BD)^2=(10)^2</p><p></p><p>9k^2/4+4k^2=100</p><p> \\ </p><p>(25k^2)/4=100</p><p> \\ </p><p>k^2=16 \\ </p><p></p><p>0k=+/-4 \\ </p><p></p><p>AC=3k=3×4=12cm. \\ </p><p></p><p>BD=4k=4×4=16cm. \\ </p><p></p><p>each side =10 cm. ,$