A rectangle of area 105cm2 has its length equal to x cm. Write down It's breadth in terms of x. Given that the perimeter is 44cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
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Area:105cm²
l=x cm
b=105/x
Now, given perimeter: 44cm
P=2l+2b⇒44=2x+210/x⇒2x²-44x+210=0
⇒2x²-30x-14x+210=0
⇒2x(x-15)-14(x-15)=0⇒(2x-14)(x-15)=0
so x=7 or x=15⇒l=7cm or 15 cm
so b=15cm or b=7cm
l=x cm
b=105/x
Now, given perimeter: 44cm
P=2l+2b⇒44=2x+210/x⇒2x²-44x+210=0
⇒2x²-30x-14x+210=0
⇒2x(x-15)-14(x-15)=0⇒(2x-14)(x-15)=0
so x=7 or x=15⇒l=7cm or 15 cm
so b=15cm or b=7cm
another way!!! perimeter=44, half of perimeter=22 it is equel to length+bredth....
so take length as (11+x) and bredth as (11-x)..
area=length*bredth(11+x)*(11-x)=105............................................................
(a+b)(a-b)=a2-b2
121-x2=105,,x2=16,,x=4
length=15,,and bredth=7
thank u!! :)
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