The perimeter of a rectangle whose length is 6 m more than its breadth is 84 m. What would be the area of a tnang e whose base is equal to the diagonal of the rectangle and wose height is equal to the length of the rectangle? (in `m^2`)

Options

A. 324
B. 372
C. 360
D. 364

Answer

C

Explanation

Let breadth of rectangle be x m
`x+xx+6+x+6=84`
`4x+12=84`
`x=18m`

`18+6=24`
`D^2=(x+6)^2+x^2`
`D^2=24^2+18^2`
`D^2=576+324=900`
`D=30 m`
Base of triangle = 30m
Height of triangle = x + 6 = 24 m
Area of triangle `=1/2xx30xx24=360 m^2`