If the side of a rhombus is `10 cm` and one diagonal is `16 cm`, then area of the rhombus is

Options

A. `24 cm^2`
B. `48 cm^2`
C. `72 cm^2`
D. `96 cm^2`

Answer

D

Explanation

Given, side of a rhombus `PQRS` is `10 cm` and one diagonal is `16 cm.`
i.e., `PQ=QR=RS=SP=10 cm` and `PR= 16 cm`

`"In" trianglePOQ, " "PQ^(2)=OP^(2)+OQ^(2)`
`["since, the diagonal of rhombus bisects each other at " 90^(@)]`
`rArr" "OQ^(2)=PQ^(2)-OP^(2)=(10)^(2)-(8)^(2)`
`rArr" "OQ^(2)=100-64=36`
`rArr" "OQ=6cm`
`["taking positive square root becuase length is always positive"]`
`therefore" "SQ=2xxOP=2xx6xx12cm`
`therefore" ""Area of the rhombus"=(1)/(2)("Product of diagonals")`
`=(1)/(2)(QSxxPR)=(1)/(2)xx12xx16=96cm^(2)`