Question

A rectangular room has a perimeter of 150m. Express its area A as a function of the width w. A. A(w) = 140w2 - w B. A(w) = 140w - 70w2 C. A(w) = 140w - w2 D. A(w) = 70w - w2

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Perimeter of the rectangular room is 150m}$

$\underline{\textsf{To find:}}$

$\textsf{The relation connecting area and width}$

$\underline{\textsf{Solution:}}$

$\textsf{Let l and w be the length and width of the rectangle}$

$\textsf{Perimeter of the rectangular room=150 m}$

$\implies\mathsf{2(l+w)=150}$

$\implies\mathsf{l+w=75}$

$\implies\mathsf{l=75-w}$

$\textsf{Area of the rectangular room}$

$\mathsf{=}\,\textsf{Length}\mathsf{\times}\textsf{Breadth}$

$\mathsf{=l{\times}w}$

$\mathsf{=(75-w){\times}w}$

$\mathsf{=75w-w^2}$

$\implies\mathsf{A(w)=75w-w^2}$

$\textsf{which is the required function}$