A rectangular hall is 10m longer than it is wide. Its floor area is 75 m². Find its length and width.

Answer 1

Answer: L=15; w=5

Set up the equation

We know that the area of the rectangle can be represented by a=lw

We know the length is 10 more than the width, but we do not know the width

The area is 75

So if you plug this information into a=lw, you should have 75=(w+10)w

75=(w+10)w Distribute the w into the parentheses

75=w²+10w subtract 75 to the other side

w²+10w-75=0 Now that it is equal to 0, we can factor. Find two number that multiply to give you -75 and add to 10

(w+15)(w-5) The opposite of the insides of the parentheses satisfy the equation, but the width can only be positive, so our answer is 5.

w=5

Now you can plug 5 in for w+10 to find the length. L=15