Answer: The length of the basement is 51 ft
Step-by-step explanation:
Knowing that the basements area is 1724 ft² we know that we have to multiply the length and the width together. Since we don't know the length we can substitute the value for X. If the width is 2/3X we would multiply it by X (the length) so our equation would look like this:
(2/3X)(X) = 1734 ----> 2/3X² = 1734
To get rid of the fraction we can multiply both sides by the reciprocal
(3/2)2/3X² = 1734(3/2)
The fractions on the left side will cancel and on the right side we will multiply 1734 by 3 then divide the product by 2.
X² = 2601
Lastly we take the square root of both sides
X = 51
