A rectangle from a cardboard of length 8 m and width 5 m

Question

A rectangle of length 8 metres and width 5 metres is cut from a square piece of cardboard . if the area of the remaining cardboard is 321, what is the length of the square piece of cardboard 

 

Answer 1

x² - 40 = 321

x² - 40 - 321 = 0

 

x = (-b ± √(b² - 4ac))/2a

x = (40 ± √(1600 - 4(1)(-321))/2(1)

x = (40 ± √(1600 + 1284))/2

x = (40 ± √2884)/2

x = (40 ± 2√721)/2

 

x = 20 + √721

x = 20 + 26.85 

x = 46.85

 

Since subtracting would result in a negative answer, we disregard.

 

46.85 m

Answer 2

Hi Tracy,

The cardboard is square, so you know all four sides are equal.

The remaining area is 321 sq.m., and an 8 x 5 or 40 sq. m. rectangle section was cut out. Add 321 + 40 = 361 sq.m. total area in the square cardboard. 

 

Since all four sides equal each other in a square, it is a square root problem. What number times itself, or squared equals 361? Take the square root of 361 sq.m. = 19 meters for each side.

 

321 + 40 = 361 sq. m.

 

√361 sq.m. = 19 meters long each side. 19 x 19 = 361 sq. meters