a triangular traffic island has a base half as long as its height. the island has an area of 121m^2. find the base and the height.

Recall that are of triangle is just

A = (1/2)bh
where
b = base
h = height
It was said that the base is half of the height, or b = (1/2)h. Substituting to the formula,
A = (1/2)(1/2)h*h
121 = (1/4)*h^2
484 = h^2
h = 22 m
Solving for the base,
b = (1/2)*22 = 11 m

Hope this helps :3

Let's solve this step by step.

Step 1: Set up the problem.
Let's assume the height of the triangular traffic island is represented by 'h' meters.
Given that the base of the traffic island is half as long as the height, we can represent it as 'b = h/2' meters.
Also, it is mentioned that the area of the triangular traffic island is 121m^2.

Step 2: Use the area formula for a triangle.
The area (A) of a triangle is given by the formula: A = (1/2) * base * height.

Step 3: Substitute the given values into the area formula.
We can substitute the values into the formula:
121m^2 = (1/2) * (h/2) * h.

Step 4: Simplify the equation.
Multiply both sides of the equation by 2 to get rid of the fraction:
242m^2 = h^2/2.

Step 5: Multiply both sides by 2 to get rid of the denominator:
484m^2 = h^2.

Step 6: Take the square root of both sides.
Taking the square root of both sides gives us:
h = sqrt(484m^2).
Simplifying further, we have h = 22m.

Step 7: Find the base.
The base (b) is given as half the length of the height, so substituting the value of h into b = h/2, we get:
b = 22m/2.
Simplifying further, we have b = 11m.

So, the height of the triangular traffic island is 22 meters and the base is 11 meters.

To find the base and height of a triangular traffic island, we can use the area formula for a triangle which is given by:

Area = (1/2) * Base * Height

Let's denote the height of the traffic island as 'h' and the base as 'b'.

Given that the base is half as long as the height, we can write the equation:

b = (1/2)h

We are also given that the area of the triangular traffic island is 121 square meters:

121 = (1/2) * b * h

Now we have two equations:

b = (1/2)h

121 = (1/2) * b * h

To solve these equations, we can substitute the value of b from the first equation into the second equation:

121 = (1/2) * ((1/2)h) * h

Simplifying the equation, we get:

121 = (1/4)h^2

Multiplying both sides of the equation by 4 to eliminate the fraction:

484 = h^2

Taking the square root of both sides:

h = √484

h = 22

Now that we found the height, we can substitute this value into the first equation to find the value of the base:

b = (1/2)h

b = (1/2) * 22

b = 11

Therefore, the base of the triangular traffic island is 11 meters and the height is 22 meters.