Question

a rectangle is 90 meter long and 60 meter wide. if strip of width 2 is added to both side, what is the area and the length of the rectangle.
length: 90 m + 2w m (because there are 2sides)
width: 60 m (original width) + 2. w m (n)
l = 90m + 2w mtrs
w = 60m + 2w meter
area:
90m + 2(-45) = 81000
90m + 0
(90m +2w)(60m+2w)
(600 + 180) +(120w +4w)

Explanation:

Step1: Define variables and new dimensions

Let \(x\) = length added to each side.
New length \(L = 70 + 2x\)
New width \(W = 60 + 2x\)

Step2: Set up area equation

Area = \(L \times W = 8600\)
$$(70+2x)(60+2x)=8600$$

Step3: Expand left-hand side

$$4200 + 140x + 120x + 4x^2 = 8600$$
$$4x^2 + 260x + 4200 = 8600$$

Step4: Simplify quadratic equation

Subtract 8600 from both sides:
$$4x^2 + 260x - 4400 = 0$$
Divide by 4:
$$x^2 + 65x - 1100 = 0$$

Step5: Solve quadratic equation

Use quadratic formula \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\), where \(a=1\), \(b=65\), \(c=-1100\):
$$x=\frac{-65\pm\sqrt{65^2-4(1)(-1100)}}{2(1)}$$
$$x=\frac{-65\pm\sqrt{4225+4400}}{2}$$
$$x=\frac{-65\pm\sqrt{8625}}{2}$$
$$x=\frac{-65\pm92.87}{2}$$
Take positive root (length can't be negative):
$$x=\frac{-65+92.87}{2}=\frac{27.87}{2}=13.935$$

Step6: Calculate new length/width

New length: \(70+2(13.935)=97.87\) m
New width: \(60+2(13.935)=87.87\) m

Answer:

The new length is approximately 97.87 meters, and the new width is approximately 87.87 meters. The length added to each side is approximately 13.94 meters.