Question

A rectangular bedroom is 4 ft longer than it is wide. Its area is 140 ft2. What is the width of the room? ft

Answer 1

w=10ft

Explanation:

You have a rectangle with an area of ​​140 square feet whose length (l) is 4 feet more than its width (w) and knowing that rectangle area is base (b) by height (h) then:

`A=b*h\\140ft^(2)= l*w \\`

but, l=w+4ft;

`140= (w+4)*w=w^(2)+4w\\w^(2)+4w-140=0`

applying cuadratic equation

`\frac{-b+-\sqrt{b^(2)-4ac}}{2a}`; where a=1, b=4 and c=-140

w1=10 and w=-14, we take w1 for being area values

finally:

width = 10 ft

Answer 2

Answer: width = 10 ft

Explanation:

Area = length × width

Let l be length and w be width

l = w + 4 ........equation (1)

From above formula

140 = l × w. ........equation (2)

Substitute equation (1) into equation (2)

140 = (w+4) × w

w^2 + 4w= 140

w^2 + 4w - 140= 0

By factorization method

(w+14)(w-10)= 0

w=-14 or w= 10

So now width is 10 ft

From equation(1)

l=w+4

l= 10+4

l= 14 ft

Width = 10 ft and length = 14 ft