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what are the length and width of a rectangle if tje length is 5meters longer than the width?the area is 126m^2.

Sagot :

We will begin solving the question by sketching the image to solve the question

Given:

The length of the rectangle is 5 meters longer than the width

The area of the rectangle is 126 square meters

This means that L=5+w

We will use the relationship:

[tex]\text{Area}=\text{length}\times width[/tex][tex]\begin{gathered} \text{Area}=(w+5)w=126 \\ \text{simplifying} \\ w^2+5w=126 \\ w^2+5w-126=0 \end{gathered}[/tex]

Simplifying further

[tex]w^2+14w-9w-126=0[/tex][tex]\begin{gathered} w(w+14)-9(w+14)=0 \\ (w+14)(w-9)=0 \end{gathered}[/tex][tex]\begin{gathered} w=9 \\ or \\ w=-14 \end{gathered}[/tex]

The width can only be positive

so that

width = 9 meters

so that the length will be w+9

Length = w+9 =9 +5 =15

Length =15 meters

Therefore

width = 9 meters

Length = 14 meters

View image AudrinnaP168852
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