Question

the length of the rectangular field is increased by 50% and its breadth is decreased by 50% to form a new rectangular field.Find the percent change in the area of the field. (With Steps|)

Answer 1

Answer:

25%

Step-by-step explanation:

We know that,

Area of a rectangle : $l \times b = lb \sf units^2$

Now,

length increases by 50%

So,

$\to l + (50\% \: {\sf {of}}\: l)$

$\to l + (\dfrac{50l}{100})$

$\to l + (\dfrac{l}{2})$

$\to l + \dfrac{l}{2}$

$\to \dfrac{2l + l}{2}$

$\to \dfrac{3l}{2} \: \sf units$

And also,

the breadth reduced by 50%

So,

$\to b - (50\% \: {\sf{of}} \: b)$

$\to b - (\dfrac{50b}{100})$

$\to b - \dfrac{b}{2}$

$\to \dfrac{2b - b}{2}$

$\to \dfrac{b}{2}$

Area of the new rectangle :

$\to \dfrac{3l}{2} \times \dfrac{b}{2}$

$\to \dfrac{3lb}{4}$

Change in area : $\sf A_1 - A_2$

Where,

• $\sf A_1$ denotes the area of original rectangle.
• $\sf A_2$ denotes the area of new rectangle i.e., after increasing and decreasing in the dimensions.

So,

$\sf\to A_1 - A_2$

$\to lb - \dfrac{3lb}{4}$

$\to \dfrac{4lb - 3lb}{4}$

$\to \dfrac{lb}{4}$

Change in% :

$\sf \to \dfrac{Change \: in \: area \times 100}{Original \: area }$

$\to \dfrac{\frac{lb}{4} \times 100}{lb}$

$\to \dfrac{lb \times 100}{4 \times lb}$

$\sf \to 25\%$

Hence, the change in area of the field is 25%