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

Answer:

Part a) $21.9\%$

Part b) $82.03\%$

Step-by-step 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

$\frac{(14)(9.5)}{(1.219)(14)(9.5)} =\frac{1}{1.219} \\ \\=0.8203$

Convert to percentage

$0.8203*100=82.03\%$