Answer:
The dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.
Step-by-step explanation:
Given,
A 1 meter steel rod is bent into a rectangle.
That means the perimeter of the rectangle is 1 meter.
So, Perimeter = ![1\ m=100\ cm](https://tex.z-dn.net/?f=1%5C%20m%3D100%5C%20cm)
Let the width of the rectangle be 'x'.
Now According to question, length exceeds quadruple its width by 5 cm.
Hence framing the above sentence in equation form, we get;
![Length=4x+5](https://tex.z-dn.net/?f=Length%3D4x%2B5)
Now we use the formula of perimeter of rectangle,
![Perimeter=2(Length+width)](https://tex.z-dn.net/?f=Perimeter%3D2%28Length%2Bwidth%29)
On substituting the values, we get;
![2(4x+5+x)=100\\\\(5x+5)=\frac{100}{2}\\\\5x+5=50\\\\5x=50-5\\\\5x=45\\\\x=\frac{45}{5}=9](https://tex.z-dn.net/?f=2%284x%2B5%2Bx%29%3D100%5C%5C%5C%5C%285x%2B5%29%3D%5Cfrac%7B100%7D%7B2%7D%5C%5C%5C%5C5x%2B5%3D50%5C%5C%5C%5C5x%3D50-5%5C%5C%5C%5C5x%3D45%5C%5C%5C%5Cx%3D%5Cfrac%7B45%7D%7B5%7D%3D9)
Now, we substitute the value of x to get the value of length;
![Length=4x+5=4\times9+5=36+5=41\ cm](https://tex.z-dn.net/?f=Length%3D4x%2B5%3D4%5Ctimes9%2B5%3D36%2B5%3D41%5C%20cm)
Thus, Width=9 cm Length=41 cm
Hence the dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.