Answered

The equation 2x(x + 8) = 110 represents the area of a rectangle.
Solve the equation. What are the approximate dimensions of the rectangle? Express your answers as decimals rounded to the nearest tenth.



Answer :

MrRoyal

The rectangle has its dimensions to be 8.8 units by 12.4 units

How to determine the dimensions of the rectangle?

From the question, the equation is given as

2x(x + 8) = 110

This equation represents the area of the rectangle

So, we have

2x(x + 8) = 110

Divide by 2

x(x + 8) = 55

Open the brackets

This gives

x² + 8x = 55

Rewrite as

x² + 8x - 55 = 0

Using a graphing calculator, we have the solutions to be

x = -12.4 and x = 4.4

The variable x cannot be negative

So, we have

x = 4.4

In 2x(x + 8) = 110, we have

Length = 2x

Width = x + 8

So, we have

Length = 2 x 4.4

Width = 4.4 + 8

Evaluate

Length = 8.8

Width = 12.4

Hence, the dimensions of the rectangle are 8.8 units by 12.4 units

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