Write a function rule for the area A of a triangle whose base, b is 2 cm less than seven times the height, h. What is the area of the triangle when the height is 14 cm?
is it
A=7h^2 - 2h / 2
??
a = 672 cm
Correct , if you use brackets in this format of typing.
A = (7h^2 - 2h) / 2
672 is also correct
The function rule for the area, A, of a triangle can be expressed as follows:
A = (1/2) * b * h
Given that the base, b, is 2 cm less than seven times the height, h, we can substitute the value of the base into the formula:
b = 7h - 2
So the function rule for the area of the triangle becomes:
A = (1/2) * (7h - 2) * h
Now we can calculate the area of the triangle when the height, h, is 14 cm:
A = (1/2) * (7 * 14 - 2) * 14
= (1/2) * (98 - 2) * 14
= (1/2) * 96 * 14
= 48 * 14
= 672 cm²
Therefore, the area of the triangle when the height is 14 cm is 672 cm².
To find the function rule for the area of a triangle, we can use the formula for the area of a triangle: A = (1/2) * base * height.
Given that the base, b, is 2 cm less than seven times the height, h, we can express the base as: b = 7h - 2.
Substituting this value of b into the formula for the area, we get: A = (1/2) * (7h - 2) * h.
Simplifying this expression, we have: A = (7h^2 - 2h) / 2.
Now, to find the area of the triangle when the height is 14 cm, we substitute h = 14 into the function rule.
A = (7h^2 - 2h) / 2
A = (7(14^2) - 2(14)) / 2
A = (7(196) - 2(14)) / 2
A = (1372 - 28) / 2
A = 1344 / 2
A = 672 cm^2
So, the area of the triangle when the height is 14 cm is 672 cm^2.
Well, you're definitely going in the right direction, but let's see if we can simplify and correct your function a bit.
The formula for the area of a triangle is A = (1/2) * base * height.
Given that the base, b, is 2 cm less than seven times the height, h, we can represent it as b = 7h - 2.
Substitute the value of b in the area formula:
A = (1/2) * (base) * height
A = (1/2) * (7h - 2) * h
A = (7h^2 - 2h) / 2
Now, let's calculate the area when the height is 14 cm:
A = (7 * 14^2 - 2 * 14) / 2
A = (7 * 196 - 28) / 2
A = (1372 - 28) / 2
A = 1344 / 2
A = 672 cm²
So, you got it right! The area of the triangle when the height is 14 cm is indeed 672 cm². Good job!