Question

A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m (see Figure). Find its length and breadth.

Answer 1

let length be `x ` m
let breadth be `(x-3) ` m
`/_ ABC ` has base = `(x-3) `m
altitude `= 12m`
area `(/_ABC = 1/2 xx (x-3) xx 12`
`= 6 (x-3) m^2`
area od DEBC`= x xx (x-3)`
`= x^2 - 3x m^2`
According to question
`(x^2 - 3x = 4 + 6(x-3)`
`x^2 - 3x = 4+6x- 18`
`x^2-9x + 14 = 0`
`x^2 - 7x - 2x + 14=0`
`x(x-7) -2(x-7)=0`
`(x-7)(x-2)=0`
`x=7,2`
Case 1 :x=7, length = `7m` & breadth`= 7-3=4m`
Case 2 : x=2, length = `2m` & breadth `=2-3=-1`
case 2 cannot be possible
so, length and breadth are `7m & 4m`
Answer