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The length of a rectangle is 23 cm less than 6 times it's width. it's area is 35 square centimeters. find the dimensions of the rectangle use the formula,area equal length times width.

User Farukh
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We are given that the area of a rectangle is 42 square meters. The formula for the area of a rectangle is:


A=wl

Where "w" is the width and "l" is the length. We are also told that the width is 5 meters longer than one-third of the length, this can be written mathematically as:


w=(1)/(3)l+5

Replacing in the formula for the area:


A=((1)/(3)l+5)l

Now we use the distributive property:


A=(1)/(3)l^2+5l

Now we replace the value of the area:


42=(1)/(3)l^2+5l

Now we subtract 42 to both sides:


(1)/(3)l^2+5l-42=0

Now we can multiply both sides by 3:


l^2+15l-126=0

Now we factor this equation, we need two numbers which sum is 15 and their product is 126, we get:


(l+21)(l-6)=0

Now we set each factor to zero:


\begin{gathered} l+21=0 \\ l=-21 \end{gathered}
\begin{gathered} l-6=0 \\ l=6 \end{gathered}

We take the positive value and therefore, the length of the rectangle is 6 meters.

To determine the width we use the relationship given by the problem:


w=(1)/(3)l+5

Replacing l = 6:


\begin{gathered} w=(1)/(3)(6)+5 \\ w=2+5 \\ w=7 \end{gathered}

The width is 7 meters.

User Mady Daby
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