To draw two different triangles with a base of 5 1/2 units and an area of 19 1/4 units², we can use the formula for the area of a triangle:
Area = 1/2 * base * height
To find the height, we can rearrange the formula:
Height = (2 * Area) / base
For the first triangle, we have a base of 5 1/2 units and an area of 19 1/4 units². Plugging these values into the formula, we get:
Height = (2 * 19 1/4) / 5 1/2
Simplifying the expression inside the parentheses, we have:
Height = (38 1/4) / 5 1/2
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we multiply 38 1/4 by 2/11:
Height = (38 1/4) * (2/11)
Converting the mixed numbers to improper fractions, we have:
Height = (155/4) * (2/11)
Multiplying the numerators and denominators, we get:
Height = (310/44)
Simplifying the fraction, we have:
Height = 7 units
So, the first triangle has a base of 5 1/2 units and a height of 7 units.
Now, let's draw the second triangle. Since we are asked to draw two different triangles, we need to change the dimensions. Let's make the base of the second triangle 5 units and the area 19 1/4 units².
Using the same formula as before, we can find the height:
Height = (2 * 19 1/4) / 5
Simplifying the expression inside the parentheses, we have:
Height = (38 1/4) / 5
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we multiply 38 1/4 by 1/5:
Height = (38 1/4) * (1/5)
Converting the mixed numbers to improper fractions, we have:
Height = (155/4) * (1/5)
Multiplying the numerators and denominators, we get:
Height = (155/20)
Simplifying the fraction, we have:
Height = 7 3/4 units
So, the second triangle has a base of 5 units and a height of 7 3/4 units.
Now, let's calculate the area of each triangle using the formula:
Area = 1/2 * base * height
For the first triangle:
Area = 1/2 * 5 1/2 * 7
Area = 1/2 * 11/2 * 7
Area = 77/4
Area = 19 1/4 units²
For the second triangle:
Area = 1/2 * 5 * 7 3/4
Area = 1/2 * 5 * 31/4
Area = 155/8
Area = 19 3/8 units²
As you can see, the area of the first triangle is 19 1/4 units² and the area of the second triangle is 19 3/8 units².