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love history [14]
3 years ago
8

A rectangular garden has an area of 22 square feet. If its length is 7 feet less than twice its​ width, find the dimensions of t

he garden.
The width of the garden is
▼
feet
cubic feet
square feet

and the length is
▼
cubic feet.
feet.
square feet.
​
Mathematics
1 answer:
DedPeter [7]3 years ago
7 0

Answer: Width is 5.5 ft, length is 18 ft

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<img src="https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B2%7D-1%7D%7B2-5a%7D%20times%20%5Cfrac%7B15a-6%7D%7Ba%5E%7B2%7D%2B5a-6%7D" id=
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\bf \cfrac{a^2-1}{2-5a}\times \cfrac{15-6}{a^2+5a-6}\\\\&#10;-----------------------------\\\\&#10;recall\quad \textit{difference of squares}&#10;\\ \quad \\&#10;(a-b)(a+b) = a^2-b^2\qquad \qquad &#10;a^2-b^2 = (a-b)(a+b)\\\\&#10;thus\quad a^2-1\iff a^2-1^2\implies (a-1)(a+1)&#10;\\\\\\&#10;now\quad a^2+5a-6\implies (a+6)(a-1)\\\\&#10;-----------------------------\\\\&#10;thus&#10;\\\\\\&#10;\cfrac{a^2-1}{2-5a}\times \cfrac{15-6}{a^2+5a-6}\implies \cfrac{(a-1)(a+1)}{2-5a}\times \cfrac{3(5a-2)}{(a+6)(a-1)}\\\\&#10;-----------------------------\\\\&#10;

\bf now\quad 3(5a-2) \iff -3(2-5a)\\\\&#10;-----------------------------\\\\&#10;thus&#10;\\\\\\&#10;\cfrac{\underline{(a-1)}(a+1)}{\underline{2-5a}}\times \cfrac{-3\underline{(2-5a)}}{(a+6)\underline{(a-1)}}\implies \cfrac{-3(a+1)}{a+6}
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