Question2. A store is to be built within a rectangular lot. The lot measures 70 m by 45 m . A lawn of uniform width, equal to the area of the store, must surround the store and be within the boundaries of the lot. How wide is the strip of lawn, to the nearest tenth? ( 6 marks)

Studdy Solution
Solve the equation:
Expand the equation:
$$3150 - 140x - 90x + 4x^2 = 1575$$
Simplify and rearrange:
$$4x^2 - 230x + 3150 = 1575$$
$$4x^2 - 230x + 1575 = 0$$
Use the quadratic formula to solve for $x$:
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
where $a = 4$, $b = -230$, $c = 1575$.
Calculate the discriminant:
$$b^2 - 4ac = (-230)^2 - 4 \times 4 \times 1575$$
$$= 52900 - 25200$$
$$= 27700$$
Calculate $x$:
$$x = \frac{230 \pm \sqrt{27700}}{8}$$
Calculate the approximate value of $x$:
$$x \approx \frac{230 \pm 166.4}{8}$$
Choose the smaller positive value:
$$x \approx \frac{230 - 166.4}{8}$$
$$x \approx \frac{63.6}{8}$$
$$x \approx 7.95$$
Round to the nearest tenth:
$$x \approx 8.0$$
The width of the strip of lawn is approximately:
$$\boxed{8.0 \, \text{m}}$$