one side of a rectangle is 10cm longer than the other. If the area of the rectangle is 375cm², show this information as a quadratic equation and hence find the length of each side
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Answer:
A be the area of rectangle , L be the length of rectangle and W be the breath of rectangle ,then
given :
L=w+10 cm
A=s6 cm2 ,
required :W=?
by using the following formula , we will get W
A=LW
56=(W+10) w
56=w2+10w
w2+10w–56 =0
then, solve the quadratic by any method that is for you
either by completing square , by factorization or by formula
now I am using by factorization
w2+10w–56 =0
w2+14w-4w-56 =0
w(w+14)-4(w+14)=0
(w+14)(w-4)=0
w+14 =0 or w-4=0
w=-14 , w=4
therefore , we omit the negative 14 because the breath is length and length is a basic physical quantity and can not be a negative
the answer : the breath of rectangle is 4 cm
checking
l=w+10= 4+10=14 cm, w=4 cm
A=lw =14 x4=56 cm2
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