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Sagot :
Let:
L = Length
W = Width
The length is 7cm longer than its width, so:
[tex]L=W+7[/tex]The area is given by:
[tex]A=W\cdot L[/tex]Therefore:
[tex]\begin{gathered} 240=(W+7)\cdot(W) \\ 240=W^2+7W \\ W^2+7W-240=0 \end{gathered}[/tex]Solve for W using the quadratic formula:
[tex]\begin{gathered} W=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ W=\frac{-7\pm\sqrt[]{7^2-4(1)(-240)}}{2(1)} \\ W=\frac{-7\pm\sqrt[]{1009}}{2} \\ W\approx12.38238 \\ or \\ W\approx-19.38238 \end{gathered}[/tex]Therefore:
W = 12.38238 since a negative width wouldn't make any sense
and:
[tex]\begin{gathered} L=W+7 \\ L=19.38238 \end{gathered}[/tex]Answer:
W = 12.38238 m
L = 19.38238 m
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