Question

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?

Answer 1

To find the area of a parallelogram, we use the formula: $a = hb$

When we plug in the givens we get: $60 = x \times (x + 7)$

Distribute the x: $60 = {x}^{2} + 7x$

Because we got an ${x}^{2}$, we need to factor the equation.

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

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: $x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$.

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

Simplify:

$x = \frac{ -7 \pm \sqrt{49 + 240 } }{2}$

$x = \frac{ -7 \pm \sqrt{289} }{2}$

$x = \frac{ -7 \pm 17 }{2}$

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

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

After finding the height, we know that base is $h+7$ so, the base is $5+7=12$.

Answer 2

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:

$\rm A=H\times B$

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.

$60=x(x+7)$

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

$x^2 +7x -60=0$

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

$x = \dfrac{-7\pm\sqrt{7^2+4\times60} }{2}$

Simplify the above expression.

$x = \dfrac{-7\pm 17}{2}$

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