Question

length of a rectangle is2 units greater it's breadth. if the area of the rectangle is 120sq. units, find its length

Answer 1

hey..

here is it answer

length of a rectane is 2 units greater than breadth.

so...

let breadth be 'X'

and then length would be 'X+2'

area would be = 120

area of a rectnagle is = length times breadth

(X)(X+2) = 120

${x}^{2} + 2x = 120$
${x}^{2} + 2x - 120 = 0$
${x}^{2} + 12x - 10x - 120 = 0$

$x(x + 12) - 10(x + 12) = 0$
$(x - 10)(x + 12) = 0$



$(x - 10) = 0$

$(x + 12) = 0$

as results shall always be positive we must take x-10

$x = 10$

breadth is 10
length is 12 as breadth + two

hope this help!

Answer 2

hi!
here is your answer .

Let the breadth of the rectangle be x.

So its length = x + 2

Area of the rectangle =120sq.cm

length × breadth = 120sq.cm.

$(x + 2)(x) = 120$

${x}^{2} + 2x = 120$

${x}^{2} + 2x - 120 = 0$

${x}^{2} + 12x - 10x - 120 = 0$

$x(x + 12) - 10(x + 12) = 0$

$(x + 12)(x - 10) = 0$

$x + 12 = 0 \: \: or \: \: x - 10 = 0$

$x = - 12 \: \: or \: \: x = 10$

but,
x = -12 is not acceptable.

$x = 10 \: units$

so.
$Breadth = 10units$

Therefore,
The breadth of the rectangle is 10 units.

length = x +2 =10 +2=12
so,
length = 12 units.


$hope \: this \: helps.$