Question

If the area of a classroom is 20m^2 if the length is increased by 3m and the width is increased by 1m the classroom will be doubled in area, determine the dimensions of the new classroom

Answer 1

Dimensions of the classroom will be $(12,\frac{5}{3})$ and (5, 4) meters.

Step-by-step explanation:

Let the length of the classroom = l meter

and the width of the classroom = w meter

Length × width = Area

l × w = 20m²  

l = $\frac{20}{w}$  ---------(1)

Length of the classroom when increased by 3 meter = l + 3

Width of the classroom when increased by 1 meter = w + 1

By increasing dimension area of the classroom gets doubled.

(l+3) (w+1) = 40 -----(2)

Now substitute l = $\frac{20}{w}$  in equation (2)

$(\frac{20}{w}+3)(w+1)=40$

$\frac{20}{w} (w+1)+3(w+1)=40$

$20+\frac{20}{w}+3w+3=40$

$\frac{20}{w}+3w=40-23$

$\frac{20}{w} +3w-17=0$

3w² - 17w + 20 = 0

3w² - 12w - 5w + 20 = 0

3w(w - 4) - 5(w - 4) = 0

(3w - 5)(w - 4) = 0

Therefore, w = $\frac{5}{3},4$

For w = $\frac{5}{3}$ from equation (1),

l = $\frac{20}{\frac{5}{3} }$

l = 12

Fro w = 4,

l = $\frac{20}{4}=5$

Therefore, there will be two sets of length and width of the classroom ($12,\frac{5}{3}$) and (5, 4)

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