A triangular traffic island has a base half as long as its height. The island has an area of 289


m2
. Find the base and the height.

Well, it seems like the traffic island could use a lesson in maintaining balance, just like a clown on stilts! Let's solve this puzzle step by step.

First, let's call the height of the triangle "x." Since the base is half as long as the height, we can say that the base is "x/2."

Now, let's use the formula for the area of a triangle: Area = (base * height) / 2. We know that the area is 289 m², so we can substitute in the values we have:

289 = (x/2 * x) / 2

To simplify the equation, let's get rid of the division by multiplying both sides by 2:

578 = x²/2

Now, let's multiply both sides again, but this time by 2 to get rid of the fraction:

1156 = x²

To solve for x, we take the square root of both sides:

x = √1156

Now, let's calculate the square root of 1156:

x ≈ 34

So, the height of the triangular traffic island is approximately 34m. Since the base is half as long as the height, the base would be approximately 34/2 = 17m.

So, the base of the triangle is approximately 17m, and the height is approximately 34m. Now, let's hope the traffic island doesn't turn into a tripping hazard for clowns!

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

Area = (base * height) / 2

Given that the area of the triangular traffic island is 289 m^2, we can set up the equation:

289 = (base * height) / 2

Now let's use the information given in the problem. It states that the base of the triangular traffic island is half as long as its height.

Let's represent the height as 'h' and the base as 'b'.

From the problem, we have:

b = (1/2)h

Now we can substitute the value of the base in terms of the height into the equation for area:

289 = (1/2)h * h

To simplify the equation, we multiply both sides by 2:

578 = h^2

Now we can solve for the value of 'h' by taking the square root of both sides of the equation:

h = sqrt(578)

Calculating the square root of 578, we get:

h ≈ 24.04

So the height of the triangular traffic island is approximately 24.04 m.

To find the base, we can substitute the value of the height into the equation we found earlier:

b = (1/2) * 24.04

b ≈ 12.02

Therefore, the base of the triangular traffic island is approximately 12.02 m.