write two equivalent expressions for the area of the figure the figure is a triangle inside the triangle it says x + 4 and the #16 is written along the length of one side of the triangle. The answer is 8(x +4) and 8x + 32 but I don't know how they got it
If the altitude is h=x+4 and the base is b=16, then the area
a = 1/2 bh = 1/2 (x+4)(16) = 8(x+4) = 8x+32
To find the area of a triangle, we usually use the formula:
Area = (base * height) / 2
In this case, the base of the triangle is the side labeled with the number 16. To find the height, we need to consider the information given inside the triangle, which states that the value of the expression x + 4 represents the height.
So, we can substitute x + 4 as the height and 16 as the base in the area formula:
Area = (16 * (x + 4)) / 2
To simplify this expression, we can start by dividing 16 by 2, which gives us 8:
Area = 8 * (x + 4)
This is the first equivalent expression for the area of the triangle: 8(x + 4).
To simplify it even further, we can distribute the 8 into the parentheses:
Area = 8x + 32
This is the second equivalent expression for the area of the triangle: 8x + 32.
To find two equivalent expressions for the area of the triangle, we need to use the formula for the area of a triangle, which is (1/2) * base * height.
In this case, the base of the triangle is 16 (as indicated by the number written along one side of the triangle), and the height is x + 4 (as indicated inside the triangle).
First Expression:
Using the formula, the area of the triangle is (1/2) * (16) * (x + 4) = 8(x + 4).
Second Expression:
We can expand the expression 8(x + 4) by multiplying 8 with both terms inside the parentheses:
8(x + 4) = 8x + (8 * 4) = 8x + 32.
Therefore, the two equivalent expressions for the area of the triangle are 8(x + 4) and 8x + 32.