Answer :
Answer:
Therefore the area of rectangle is increased by 15.5%.
Step-by-step explanation:
Assume the length and width of the rectangle be x and y respectively.
The area of the rectangle is = length×width
=xy.
Now the length of the rectangle is increased by 10%.
Then the length of the rectangle increased = [tex]x\times \frac{10}{100}[/tex].
New length of the rectangle is [tex]=x+\frac{10x}{100}[/tex]
[tex]=\frac{100x+10x}{100}[/tex]
[tex]=\frac{110x}{100}[/tex]
The width of the rectangle is increased by 5%.
Then the width of the rectangle increased = [tex]y\times \frac{5}{100}[/tex].
New length of the rectangle is [tex]=y+\frac{5y}{100}[/tex]
[tex]=\frac{100y+5y}{100}[/tex]
[tex]=\frac{105y}{100}[/tex]
New area of the rectangle is = [tex]\frac{110x}{100}\times\frac{105y}{100}[/tex]
= 1.155 xy.
The percentage of area increase is
[tex]=\frac{\textrm{New area - Original area}}{\textrm{Original area}}\times 100[/tex]
[tex]=\frac{1.155xy-xy}{xy}\times 100[/tex]
[tex]=\frac{0.155xy}{xy}\times 100[/tex]
=15.5.
Therefore the area of rectangle is increased by 15.5%.