Answer:
The dimensions of the original rectangle are Length =12cm, Width=8cm
Step-by-step explanation:
Let the length of the rectangle be x
Let the width of the rectangle be y
The perimeter of a rectangle is 40cm.
2(x+y)=40
Divide both sides by 2
x+y=20
If the length were doubled(2x) and the width halved(y/2), the perimeter would be increased by 16cm,i.e.(40+16)cm
Therefore:
[tex]2(2x+\dfrac{y}{2})=56[/tex]
Divide both sides by 2
[tex]2x+\dfrac{y}{2}=28[/tex]
From the first equation, x=20-y.
Substitute x=20-y into [tex]2x+\dfrac{y}{2}=28[/tex]
[tex]2x+\dfrac{y}{2}=28[/tex]
[tex]2(20-y)+\dfrac{y}{2}=28\\\dfrac{4(20-y)+y}{2}=28\\80-4y+y=56\\-3y=-24\\$Divide both sides by -3\\y=8cm\\Recall:x=20-y\\x=20-8=12cm\\The dimensions of the original rectangle are Length =12cm, Width=8cm[/tex]
