Question

A rectangular building measuring 30 m by 25 m is going to have its area increased by 200 m² by adding a strip of uniform width to all four sides. Determine the width of the strip

Answer 1

Step-by-step explanation:

We can model the situation as:

So, we need to calculate the value of x.

Now, we know that the area will be increased by 200 m², so the initial area is:

25 m * 30 m = 750 m²

It means that the new area should be:

750 + 200 = 950 m²

Then, we know that the new area is also equal to the length times the width, so the new area is:

(25 + x + x) * (30 + x + x) = 950

Solving for x, we get:

`\begin{gathered} (25+x+x)\cdot(30+x+x)=950 \\ (25+2x)\cdot(30+2x)=950 \\ (25\cdot30)+(25\cdot2x)+(2x\cdot30)+(2x\cdot2x)=950 \\ 750+50x+60x+4x^2=950 \\ 4x^2+110x+750-950=0 \\ 4x^2+110x-200=0 \end{gathered}`

Now, we have a quadratic function, so the solutions of the function can be calculated as:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Where a is the number beside x², b is the number beside x and c is the constant.

Replacing, we get:

`\begin{gathered} x=\frac{-110\pm\sqrt[]{110^2-4\cdot4\cdot(-200)}}{2\cdot4} \\ x=1.71 \\ or \\ x=-29.21 \end{gathered}`

Since x = -29.21 has no sense in this situation, the width of the strip is 1.71

Answer: 1.71 m