A rectangular hall is 10m longer than it is wide. It’s floor area is 75m ‘squared’. Find it’s length and width.

Question

explanation, step by step and working out please.

Answer 1

Area = Length*width

LW = 75

 

Since it is 10m longer than it is wide, L = w + 10.

Substitute that into the area equation.

 

(w+10)(w) = 75

distribute the w through the parenthesis

w² + 10w = 75

subtract 75 from both sides

w² + 10w - 75 = 0

 

We can factor this.  The factors of -75 that add to 10 are 15(-5)

 

w² + 10w - 75 = 0

(w+15)(w-5) = 0

Either w+15 = 0 and w = -15

Or

w-5 = 0 and w = 5

 

Since width will be a positive quantity, discard the negative.

The width is 5 m

L = w+10 = 15 m

 

The hall is 15m long and 5m wide.