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The length of a rectangle is the width minus 5 units. The area of the rectangle is 36 units. What is the width, in units, of the rectangle

Respuesta :

calculista

Answer:

The width of the rectangle is  [tex]9\ units[/tex]

Step-by-step explanation:

Let

x----> the length of rectangle

y----> the width of rectangle

we know that

The area of rectangle is equal to

[tex]A=xy[/tex]

[tex]A=36\ units^{2}[/tex]

so

[tex]36=xy[/tex] ------> equation A

[tex]x=y-5[/tex] -----> equation B

substitute equation B in equation A and solve for y

[tex]36=(y-5)y[/tex]

[tex]y^{2}-5y-36=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]y=9\ units[/tex]

see the attached figure

therefore

The width of the rectangle is  [tex]9\ units[/tex]

Ver imagen calculista
JeanaShupp

Answer: 9 units.

Step-by-step explanation:

Let x be the width of the rectangle .

Then, the length would be x-5.

Area of rectangle = Length x Breadth

[tex]=(x-5)x=x^2-5x[/tex]

Since ,  The area of the rectangle is 36 units.

[tex]\Rightarrow\ x^2-5x=36\\\\\Rightarrow\ x^2-5x-36=0\\\\\Rightarrow\ x^2-9x+4x-36=0\\\\\Rigtarrow\ x(x-9)+4(x-9)=0\\\\\Rightarrow\ (x-9)(x+4)=0\\\\\Rightarrow\ x=9 , -4[/tex]

But width cannot be negative , so width = x= 9 units

Hence, the width of the rectangle = 9 units.

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