Verified answer

QUADRATIC INEQUALITY

Problem:

The governor is planning to construct a new park. The length of the park is 24 m longer than it is wide. Suppose the area of the park does not exceed 1,456 square meters, what are the largest possible dimensions of the park?

Answer: The largest possible dimensions of the park is 28 meters by 52 meters.

Step-by-step explanation:

We can express this in the inequality: A ≤ 1,456 where A refers to the area of the new park to be constructed.

Since, the area of park (assuming that it is rectangular in shape) can be computed by multiplying the length and the width, and let L be the length of the park while W be the width but L = 24 + W, so by directly substituting to the inequality:

A ≤ 1,456

LW  ≤ 1,456

(24+W)W  ≤ 1,456

By quadratic formula, the two values of the root are 28 and -52 but we will only consider the positive root. So, the measure of the width is 28 meters. On the other hand, L = 24 + W = 24 + 28 = 52. Hence, the measure of the length is 52 meters. If you recheck the area:

A = 28x52

A = 1,456 square meters

And this does not exceed the requirement of the new park to have an area not exceeding 1,456 meters.

Read more about quadratic inequality:

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