Answer:
When l = 6 ⇒ w = 4
when l = 4 ⇒w = 6
Step-by-step explanation:
We have given perimeter and area of rectangle.
Perimeter = P = 20 inches and Area = A = 24 square inches
We have to find the length and width of the rectangle.
Let l is length and w is width of rectangle.
The formula of Perimeter is :
P = 2(l+w)
The formula of area is :
A = l × w
Given values :
P = 2(l+w) = 20
l+w = 10
w = 10-l eq(1)
A = l × w = 24 eq(2)
Putting eq(1) in eq(2), we have
A = l × (10-l) = 24
10l-l² = 24
l²-10l +24= 0
Applying factorization to above equation, we have
(l-6)(l-4) = 0
Applying Zero-Product rule , we have
l-6 = 0 or l-4 = 0
l = 6 or l = 4
Putting above values in eq(1) , we have
When l = 6 ⇒ w = 10-6
w = 4
when l = 4 ⇒w = 10-4
w = 6
Answer is :
When l = 6 ⇒ w = 4
when l = 4 ⇒w = 6
