Certainly! Let's solve this step-by-step.
1. Define the variables:
- Let [tex]\( l \)[/tex] be the length of the rectangle.
- Let [tex]\( b \)[/tex] be the breadth of the rectangle.
2. Given conditions:
- The perimeter of the rectangle is [tex]\( 40 \)[/tex] meters.
- The length ([tex]\( l \)[/tex]) is 4 meters less than 5 times the breadth ([tex]\( b \)[/tex]).
3. Formulate the equations:
- The formula for the perimeter of a rectangle is [tex]\( P = 2(l + b) \)[/tex].
- Given [tex]\( P = 40 \)[/tex], we have:
[tex]\[
2(l + b) = 40
\][/tex]
4. Express the length in terms of the breadth:
- According to the problem, [tex]\( l = 5b - 4 \)[/tex].
5. Substitute [tex]\( l = 5b - 4 \)[/tex] into the perimeter equation:
[tex]\[
2((5b - 4) + b) = 40
\][/tex]
6. Simplify the equation:
[tex]\[
2(6b - 4) = 40
\][/tex]
7. Distribute the 2 over the terms inside the parenthesis:
[tex]\[
12b - 8 = 40
\][/tex]
8. Solve for [tex]\( b \)[/tex]:
- Add 8 to both sides of the equation:
[tex]\[
12b = 48
\][/tex]
- Divide both sides by 12:
[tex]\[
b = 4
\][/tex]
9. Find the length using the breadth:
- Substitute [tex]\( b = 4 \)[/tex] back into the equation [tex]\( l = 5b - 4 \)[/tex]:
[tex]\[
l = 5(4) - 4
\][/tex]
[tex]\[
l = 20 - 4
\][/tex]
[tex]\[
l = 16
\][/tex]
10. Conclusion:
- The length of the rectangle is [tex]\( 16 \)[/tex] meters.
