A triangle is cut from a rectangle. The height of the triangle is half of the unknown side length ss. The area of the shaded region is 84 square inches. Write an equation you can use to find the side length ss.
An equation is
__________
=84
Help me with an equasion
A triangle is cut from a 14 in by 12 in rectangle. The triangle is cut so the 12 in side is now only 6in. Therefor, the new area is 84 square ft. What is an equation to represent this word problem?
To find the equation, we need to determine the area of the shaded region.
Let's denote the unknown side length of the rectangle as s. Since the height of the triangle is half of s, the height can be written as s/2.
The area of the shaded region is the area of the rectangle minus the area of the triangle. The area of the rectangle is s * s = s^2, and the area of the triangle is (1/2) * (s/2) * s/2 = (1/4) * s^2.
Therefore, the equation to find the side length is:
s^2 - (1/4)s^2 = 84
Simplifying the equation:
(3/4)s^2 = 84
Now, we can solve for s:
Multiply both sides of the equation by (4/3):
s^2 = (4/3) * 84
Divide both sides of the equation by (4/3):
s^2 = 112
Take the square root of both sides to find the value of s:
s = √112 or s ≈ 10.6
So, the equation you can use to find the side length s is s^2 - (1/4)s^2 = 84.