We are told that the height of a parallelogram is 4mm more than its base. Therefore, if we let b be the base, the height can be expressed as h=b+4. We are also told that the area is 221 square millimeters. Let's draw a diagram to illustrate the situation.
The area of a parallelogram is the product of its base and its height.
A=bhWe can substitute A= 221 and h= b+4 into this formula and solve for b, the base of the parallelogram. Let's do it!
Note it's a quadratic equation. To solve this equation we will use the Quadratic Formula.
ax^2+ bx+ c=0 ⇕ x=- b± sqrt(b^2-4 a c)/2 a
The variable in our equation is b. Let's replace it with x not to mistake it with the b in the Quadratic Formula.
b^2+4b-221=0
⇕
x^2+4x-221=0
Next, we need to identify the values of a, b, and c.
x^2+4x-221=0 ⇕ 1x^2+ 4x+( - 221)=0
We see that a= 1, b= 4, and c= - 221. Let's substitute these values into the Quadratic Formula.
Now, we can go back to the previous notation and replace x with b. The solutions of our equation are b=- 2 ± 15. Let's separate them into the positive and negative cases.
b=- 2 ± 15
b_1=- 2+15
b_2=- 2-15
b_1=13
b_2=- 17
Since b is the length base of a parallelogram it must be positive. Therefore, the base of the parallelogram is 13mm. The height is 4mm more than its base, so we can add 4 to 13 to obtain the height.
Height: 13+4=17 mm
