Question

If the area of a rectangle is 84 sqcm and the difference of its length and breadth is 5cm,find its length,breadth and perimeter?

The eighth qstn in the two sums I have doubt pls help

Answer 1

Length, Breath `= 12, 7` (cm)
Perimeter `= 38` (cm)

Explanation:

If the longer side is called the length and the length is called `L`; call the breadth `B`.

Then we are told:
[1]`color(white)("XXX")B=L+5` (cm)
and
[2]`color(white)("XXX")B * L = 84` (sq.cm.)

Substituting `(L+5)` from [1] for `B` in [2]
[3]`color(white)("XXX")(L+5) * L =84`

[4]`color(white)("XXX")L^2+5L =84`

[5]`color(white)("XXX")L^2+5L-84=0`

[6]`color(white)("XXX")(L+12)(L-7)=0`

[7]#color(white)("XXX"){:(L=-12,color(white)("X")orcolor(white)("X"),L=7), ("impossible",,):}#

Since `B=L+5`
`color(white)("XXX")B=12`

`"Perimeter " = 2xx ("Length" + "Breadth")=2xx(7+12)=38`