Question

Two sandboxes with the same area are shown. The equation w(3w+1)=5^2 represents the area of Sandbox 2 in terms of its width. Which is the approximate length of the longest side of Sandbox 2? Round the answer to the nearest hundredth of a meter.
A.) 2.72 meters

B.) 3.06 meters

C.) 9.16 meters

D.) 10.18 meters

Answer 1

sandbox 1 area = 5*5 = 25 square m

sandbox 2

25=w*(3w+1)=

3w^2+w-25=0

w=2.7248 (round to 2.72 m)

2.72*3=8.16+1 = 9.16

Longest side = 9.16 meters

Answer 2

Answer:

C.) 9.16 meters

Step-by-step explanation:

We are given that the two sandboxes have same area and the equation is given by 25 = w*(3w+1).

Now, we simplify this equation in order to find the value of unknown variable 'w'.

i.e. 25 = 3$w^{2}$+w

i.e. 3$w^{2}$+w-25=0

The two factors of this quadratic equation are w=2.72 and w= -3.05.

But, as 'w' represents the length of the box, so it cannot be negative.

Therefore, w = 2.72

So, the longest side of the box is (3w+1) = 3*2.72+1 = 9.16 meter

Hence, the length of longest side to the nearest hundredth is 9.16 meter.