Question

Hi need help on hw plz help me out my questions is - a rectangle has a length of 14cm and width 9.5cm the length increased by 6% and the width increased by 15%. a) Calculate the percentage change in area of the rectangle. b) what is the original area as a percentage of the increased area of the rectangle?- plz can u show steps how to work these 2 questions out pleasee

Answer 1

Part a)
`21.9\%`

Part b)
`82.03\%`

Explanation:

we know that

The original area of rectangle is equal to

`A=(14)(9.5)\ cm^(2)`

so

if the length is increased by 6% and the width is by 15%

then

the new area is equal to

`A=[1.06(14)][1.15(9.5)]\ cm^(2)`

`A=(1.06*1.15)(14)(9.5)\ cm^(2)`

`A=(1.219)(14)(9.5)\ cm^(2)`

The new area is (1.219) times the original area

Part a) Calculate the percentage change in area of the rectangle

`1.219-1=0.219`

convert to percentage

`0.219*100=21.9\%`

Part b) what is the original area as a percentage of the increased area of the rectangle?

Divide the original area by the increased area

`((14)(9.5))/((1.219)(14)(9.5)) =(1)/(1.219) \\ \\=0.8203`

Convert to percentage

`0.8203*100=82.03\%`