Question

The base of an open rectangular box is of length (2x+5) cm and width x cm. The area of this base is 58cm^2. The height of the open box is (x-2) cm.
a) show that 2x^2+5x-58=0
b) solve the equation in the question above, giving your answer to 2 decimal places
c) calculate the volume of the box, stating units of you answer

Answer 1

Answer:

Part A )

x(2x+5) = 58cm²

2x²+5x=58cm²

2x²+5x-58=0

Part B )

x=4.28

x= -6.78

Has to be positive so x=4.28

Part C)

58x2.28 = 132.24cm³

Step-by-step explanation:

For Part A - Self explanatory, do length (2x+5) x width (x) which equals to 58cm^2 then rearrange to make the equation equal to 0 so 58 goes to the left side.

For Part B - Solve the quadratic using the formula, a = 2, b = 5, c = -58 and you should get two answers. A length cannot be negative thus must be the positive answer. Some students only write 4.28 and this doesn't get full marks for you have to explain why.

For Part C - a common mistake tends to be the student does ((4.28x2)+5) x 4.28 x (4.28-2). You do not need to work out the area for it is given to you (58cm^2), thus just multiply the area by height as V= length x width x height