Question

please tell me the answer for this
​

Answer 1

Answer:

☞The diagonals of a rhombus bisect each-other at right angles,with the side of the rhombus being the hypotenuse . Half the lengths of the diagonals AO = 12 cm , BO= 16 cm. and the hypotenuse(AB) in right triangle ABO in  rhombus ABCD.

AB²=(Hypotenuse side), AO = 12² BO = 16²

Using Pyhagoras Theorem for the right-angled triangle ABO,

AB²= AO²+ BO²

h² = 12² + 16²

h²= 144+256

h²= 400

h = 20

∴ The length of the side of the rhombus is 20 cm.

Area of a rhombus = $\frac{1}{2}×d_1×d_2$

Area of a rhombus= base × height

∴ Comparing both formulas

$\frac{1}{2}×24×32 = 20×h$ (base is side of the rhombus)

12×32 = 20×h

h = 12×38/20

h = 384/20

h = 19.2 cm

∴ Option d) 19.2 is the correct option

HOPE IT HELPS ✌

$\sf \fbox \orange{@MrLegend}$

$\sf \fbox \green{Thank You!!!}$