Question

A rectangular animal shed needs to be fenced. if the required fencing is 100ft. and p represent the length of the shed, write an expression for the Area of the shed in terms of p​

Answer 1

Step-by-step explanation:

$\color{purple} \begin{aligned} &\text{Solution: } \text{We know that the perimeter of a rectangle \( =2 \) (length + breadth) } \\ \\ & \text{Let the breadth of the animal shed be \( q \).} \\ \\ &\text{ So, perimeter \( =2 \times(p+q) \) } \\ \\ &\text{\( \Rightarrow 100=2 p+2 q \)} \\ \\ &\Rightarrow q=\frac{1}{2}(100-2 p) \\ \\ & \text{Area of the shed =length \(\times \) breadth} \\ \\ &\[ =p \times \frac{1}{2}(100-2 p)=50 p-p^{2} \] \\ \\ & \text{Therefore, area of the shed is} \left(50 p-p^{2}\right) \text{ sq. units.}\end{aligned}$