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You decide to build a rectangular garden in your backyard. You've designated an area of 180m^2 for your garden. Due to the configuration of your backyard, the width of the garden must be 8 meters less than the length.

Respuesta :

MrRoyal

Answer:

[tex]Length = 18m[/tex]

[tex]Width = 10m[/tex]

Step-by-step explanation:

Given

[tex]Area = 180m^2[/tex]

[tex]Width = Length - 8[/tex]

Required

Determine the Length and the Width

Represent Width with W and Length with L;

So, we have:

[tex]Area = L * W[/tex]

[tex]Area = L * (L - 8)[/tex]

[tex]180 = L * (L - 8)[/tex]

[tex]180 = L^2 - 8L[/tex]

[tex]L^2 - 8L - 180 = 0[/tex]

Expand

[tex]L^2 - 18L + 10L- 180 = 0[/tex]

[tex]L(L - 18) + 10(L- 18) = 0[/tex]

[tex](L + 10)(L- 18) = 0[/tex]

Split

[tex]L + 10 =0[/tex] or [tex]L - 18 = 0[/tex]

[tex]L = -10[/tex] or [tex]L = 18[/tex]

But length cant be negative:

So,

[tex]L = 18[/tex]

Recall that:

[tex]Width = Length - 8[/tex]

[tex]W = 18 - 8[/tex]

[tex]W = 10[/tex]

Hence:

[tex]Length = 18m[/tex]

[tex]Width = 10m[/tex]

abidemiokin

The dimension of the rectangular garden is 8m by 10m

The formula for calculating the area of the rectangular garden is expressed as;

A = lw

l is the length

w is the width

If the width of the garden must be 8 meters less than the length, then;

w = l - 8

Substitute into the formula;

180 = l(l-8)

180 =l^2 - 8l

l^2-8l - 180 = 0

Factorize the result;

l(l+10)-8(l+10) = 0

(l-8)(l+10)=0

l = 8 and -10

Since A = lw

w = A/l

w = 180/8

w = 10

Hence the dimension of the rectangular garden is 8m by 10m

Learn more on area of the rectangle here:https://brainly.com/question/17416965

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