Question

If each of the dimensions of a rectangle is incresed by 100%, then the area is increased by
a) 400%
b) 100%
c) 200%
d) 300%
(Explain with solution)​

Answer 1

✬ Percentage Increased = 300% ✬

Step-by-step explanation:

Given:

• Each dimensions of rectangle is increased by 100%.

To Find:

• How much area is increased?

Solution: Let the length of rectangle be x and breadth be y.

As we know that

★ Ar. of Rectangle = Length × Breadth ★

So area of this rectangle will be xy.

• Now length is increased by 100%

➟ New length = x + 100% of x

➟ x + 100/100 × x

➟ x + x = 2x

➟ New breadth = y + 100% of y

➟ y + 100/100 × y

➟ y + y = 2y

∴ New area = New length × breadth

• New area = 2x × 2y = 4xy

Total change in area = (New – old) area

Total change = 4xy – xy = 3xy

Now percentage change will be

• Total change/Original × 100

➮ Percentage change = 3xy/xy × 100

➮ 3 × 100

➮ 300 %

Hence, area will be increased by 300%.

(Option D is correct)