Question

Given the following rectangle and circle, at what approximate value of x are the two areas equal? x ≈ 5.8 x ≈ 3.4 The curves do not intersect, so there is no solution. x ≈ 8.7

Answer 1

The approximate value of x will be approximately equal to 3.4

Area of triangle and circle

The formula for calculating area of rectangle is expressed as:

A  = lw

• l is the length
• w is the width

Ar = (3x-1)(x+2)

Ar = 3x^2+6x-x-2

Ar = 3x^2 + 5x - 2

For the circle

Ac = πr²

Ac = 3.14(x-3)²

Ac = 3.14(x²-6x+9)

Ac = 3.14x² - 18.84x + 28.26

If the area are equal;

3x² + 5x - 2 = 3.14x² - 18.84x + 28.26

3.14x² - 3x² - 5x - 18.84x + 30.26 = 0
0.14x²-23.84x+30.26 = 0

On factorizing the equation, the approximate value of x will be approximately equal to 3.4

Learn more on area of rectangle here; brainly.com/question/25292087