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Select the correct answer from each drop-down menu.
The length of a rectangle is 5 inches more than its width. The area of the rectangle is 50 square inches.
The quadratic equation that represents this situation is
The length of the rectangle is
inches.

Respuesta :

calculista

Answer:

Part 1) The quadratic equation is [tex]x^{2}-5x-50=0[/tex]

Part 2) The length of rectangle is 10 in and the width is 5 in

Step-by-step explanation:

Part 1)

Find the quadratic equation

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=50\ in^{2}[/tex]

so

[tex]50=xy[/tex] -----> equation A

[tex]x=y+5[/tex]

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

substitute equation B in equation A

[tex]50=x(x-5)\\50=x^{2} -5x\\ x^{2}-5x-50=0[/tex]

Part 2) Find the length of the rectangle

[tex]x^{2}-5x-50=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=10\ in[/tex]

see the attached figure

Find the value of y

[tex]y=10-5=5\ in[/tex]

therefore

The length of rectangle is 10 in and the width is 5 in

Ver imagen calculista
david8644

Answer:

Quadratic equation: [tex]x^{2} +5x-50=0[/tex]

Length of the rectangle: 10 inches.

Step-by-step explanation:

In order to solve this you just have to factorize the equation to solve the different values for X:

[tex]x^{2} +5x-50=0\\(x+10)(x-5)=0[/tex]

So the only possible answer for the problem would be 5, so if the width is equal to X and the length is x+5 then the length of the rectangle would be 5+5 and that would be 10.

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