Question

A room is 5m longer than its breadth. if the area of the floor of the room is 150sqm. find the length and breadth of the room

Answer 1

Answer:

breadth=10 and length=15

Step-by-step explanation:

let breadth be x. then length is x+5,

now area of rectangle= length×breadth

but,

area of rectangle=150m²(given in question)

now, 150=x(x+5)

150=x²+5x

x²+5x-150=0

x²+(15x-10x)-150=0

x²+15x-10x-150=0

x(x+15)-10(x+15)=0

(x+15)(x-10)=0

x=10,-15

so, breadth=10 and length=15

Answer 2

$\sf\large\underline\blue{Given:}$

$\tt{\implies Area\:_{(room)}=150m^2}$

$\sf\large\underline\blue{To\: Find:}$

$\tt{\implies Room\:_{(length\:and\: breadth)}=?}$

$\sf\large\underline\blue{Solution:}$

• To calculate the length and breadth of room , at first we have to assume the breadth of room be x and the length of room be x+5. By applying formula of rectangle to calculate length and breadth of room:]

$\sf\large\underline\green{Here\:, length=x+5\:\: breadth=x:}$

$\sf\large\underline\blue{Formula\: used:}$

$\tt{\implies Area\:_{(room)}=length*breadth}$

$\tt{\implies (x+5)*x=150}$

$\tt{\implies x^2+5x=150}$

$\tt{\implies x^2+5x-150=0}$

• Here, splitting the middle term:]

$\tt{\implies x^2+15x-10x-150=0}$

$\tt{\implies x(x+15)-10(x+15)=0}$

$\tt{\implies (x+15)(x-10)=0}$

$\tt{\implies \therefore\:x=-15\:and\:10}$

• Here we can't take the value of x having negative because the length or breadth of room can't be negative so, we take x=10:]

$\sf\large{Hence,}$

$\tt{\implies Length\:_{(room)}=x+5=10+5=15m}$

$\tt{\implies Breadth\:_{(room)}=x=10m}$