Question

The area of a rectangle is $15$ square centimeters and the perimeter is $16$ square centimeters. What are the dimensions of the rectangle?

Answer 1

From the given information we know that the area of a rectangle is,
area = $(l\times b)$
15 = $(l\times b)$.......(i)
The perimeter of a rectangle is,
$p=2(l+b)$
$16=2(l+b)$
$(l+b)=8$
or $l=8-b$....(ii)
Now here we substitute the value of $l$ in the first equation, so we get the new equation as,
$(8-b)\times l=15$
or $8b-b^2=15$
or $b^2-8b+15=0$
When we factorize this trinomial we get,
$(b-3)(b-5)=0$
To substitute the value of $b$ in such a way that one of the fractions becomes 0 to get the LHS also 0 we have two options:
$b$ = 3 so the value of $l$ = 5
or $b$ = 5 so the value of $l$ = 3
but as we know that the length is always bigger than the width, so the first option is right.
Hence the length of the given rectangle = 5cm
ans the width of the given rectangle is = 3cm