Question

A Rectangle has a length that is one foot longer than it’s width. If the area of the rectangle is 210ft^2 what are the dimensions?

Answer 1

Required Answer:-

Let

`\qquad\quad {:}\longmapsto\sf The\: breadth =x\: ft`

`\qquad\quad {:}\longmapsto\sf The\:length=x+1ft`

`\qquad\quad {:}\longmapsto\sf Area=210ft^2`

• As we know that in a rectangle

`{\boxed {\sf Area=length* Breadth}}`

• Substitute the values

`\qquad\quad {:}\longmapsto\sf x (x+1)=210`

`\qquad\quad {:}\longmapsto\sf x^2+x=210`

`\qquad\quad {:}\longmapsto\sf x^2+x-210=0`

• Factorise

`\qquad\quad {:}\longmapsto\sf x^2+15x-14x-210=0`

`\qquad\quad {:}\longmapsto\sf x (x+15)-14 (x+15)=0`

`\qquad\quad {:}\longmapsto\sf (x+15)(x-14)=0`

`\qquad\quad {:}\longmapsto\sf x+15=0\:or\:x-14=0`

`\qquad\quad {:}\longmapsto\sf x=-15\:or\:x=14`

• In menstruation there is no negative value .
• So (x=-15) can't be possible.

Hence correct value

`\qquad\quad {:}\longmapsto\sf x=14`

__________________________

`\qquad\quad {:}\longmapsto\sf Breadth =x=14ft`

`\qquad\quad {:}\longmapsto\sf Length=x+1=14+1=15ft`