Question

Charlie's garage has a rectangular floor space. Its length is 3 times its width. Charlie extends the width of his garage to 6 m, providing a floor area of 45 m2. what is the percentage

Answer 1

Answer:

The percentage change is 140%

Step-by-step explanation:

Given

$L= 3W_1$ ---- initial dimension

$W_2 = 6m$ --- new width

$A_2 = 45m^2$ --- new dimension

Required

The percentage increment

The length remains constant because only the width is extended.

The new area is:

$Area =Length * Width$

$A_2=L * W_2$

Make L the subject

$L = \frac{A_2}{ W_2}$

Substitute values for A and W

$L = \frac{45m^2}{6m}$

$L = \frac{45m}{6}$

$L = 7.5m$ --- this is the length of the garden

Calculate the initial width:

$L= 3W_1$

Make W1 the subject

$W_1 = \frac{1}{3} * L$

$W_1 = \frac{1}{3} * 7.5$

$W_1 = 2.5$

So, the initial area is:

$A_1 = L_1 * W_1$

$A_1 = 2.5 * 7.5$

$A_1 = 18.75$

The percentage change in area is:

$\%A = \frac{A_2 - A_1}{A_1}$

$\%A = \frac{45 - 18.75}{18.75}$

$\%A = \frac{26.25}{18.75}$

$\%A = 1.4$

Express as percentage

$\%A = 1.4*100\%$

$\%A = 140\%$