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help to solve this word problem?

the width of a rectangle is 7 feet less than its length. if the area of the rectangle is 170 square feet, then find the length and width.

Respuesta :

Let's assume

length =l

width =w

we are given

the width of a rectangle is 7 feet less than its length

so, we get

[tex] w=l-7 [/tex]

now, we know that

area = length*width

[tex] A=l*w [/tex]

now, we can plug w

[tex] A=l*(l-7) [/tex]

we have

Area=170

[tex] 170=l*(l-7) [/tex]

[tex] l^2-7l-170=0 [/tex]

now, we can factor it

[tex] (l-17)(l+10)=0 [/tex]

now, we can solve for l

[tex] (l-17)=0 [/tex]

[tex] length=17 feet [/tex]

now, we can find width

[tex] w=17-7 [/tex]

[tex] width=10 feet [/tex]

so, dimensions are

[tex] length=17 feet [/tex]

[tex] width=10 feet [/tex]...............Answer