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The base of a parallelogram is 7 ft more than the height. If the area of the parallelogram is 60ft square, what are the measures of the base and the height?

The base of a parallelogram is 7 ft more than the height If the area of the parallelogram is 60ft square what are the measures of the base and the height class=

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To find the area of a parallelogram, we use the formula: [tex]a = hb [/tex]

When we plug in the givens we get: [tex]60 = x \times (x + 7)[/tex]

Distribute the x: [tex]60 = {x}^{2} + 7x[/tex]

Because we got an [tex] {x}^{2} [/tex], we need to factor the equation.

Turn the equation into standard form by subtracting 60 from both sides: [tex] {x}^{2} + 7x - 60 = 0[/tex]

Now, we can factor this by using the quadratic formula.

Quadratic formula is pure memorizing so I don't like it. But it is very useful because it works all the time. The template for it is: [tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex].

When we plug in the values in the standard form we get: [tex]x = \frac{ -7 \pm \sqrt{ {7}^{2} - 4 \times 1 \times (- 60)} }{2 \times 1} [/tex]

Simplify:

[tex]x = \frac{ -7 \pm \sqrt{49 + 240 } }{2} [/tex]

[tex] x = \frac{ -7 \pm \sqrt{289} }{2} [/tex]

[tex] x = \frac{ -7 \pm 17 }{2} [/tex]

Now, we need to branch out the plus-minus sign: [tex]x = \frac{ - 7 + 17}{2} \: \: x = \frac{ - 7 - 17}{2} \\ \\ x = \frac{10}{2} \: \: x = \frac{ - 24}{2} \\ \\ x = 5 \: \: x = - 12[/tex]

Because a measurement can't be negative, 5 is the height.

After finding the height, we know that base is [tex]h+7[/tex] so, the base is [tex] 5+7=12[/tex].

The height of the parallelogram is 5 ft and the base of the parallelogram is 14 ft and this can be determined by forming the quadratic equation by using the given data.

Given :

  • The base of a parallelogram is 7 ft more than the height.
  • The area of the parallelogram is 60ft square.

Let the height of the parallelogram be 'x' then the base of the parallelogram is (x + 7).

The area of the parallelogram is given by the formula:

[tex]\rm A=H\times B[/tex]

where A is the area, B is the Base and H is the height of the parallelogram.

Now, substitute the values of known terms in the above formula.

[tex]60=x(x+7)[/tex]

Simplify the above expression in order to determine the value of 'x'.

[tex]x^2 +7x -60=0[/tex]

By using the quadratic formula the factors of the above equation can be determined.

[tex]x = \dfrac{-7\pm\sqrt{7^2+4\times60} }{2}[/tex]

Simplify the above expression.

[tex]x = \dfrac{-7\pm 17}{2}[/tex]

x = -12 or 5

'x' is never negative. So, the value of 'x' is 5 ft.

The base of the parallelogram is (7+7) 14 ft.

For more information, refer to the link given below:

https://brainly.com/question/1563728

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