the area of a triangle is 147 square inches and its height is 1.5 times its base. find the base and the height of the trianle.

let the base be x

then the height is 3x/2

(1/2)(3x/2)(x) = 147
x^2 = 196
x = √196 = 14

so base is 14
height = 21

check: (1/2)(14)(21) = 147

Well, it seems like we have a serious mathematical situation here. But don't worry, I can still add a dash of humor to it!

Let's solve this triangle puzzle together. We know that the area of the triangle is 147 square inches, and the height is 1.5 times the base. So, let's call the base "B" (because it's the base of our problem) and the height "H" (because it's high time we find it).

We can use the formula for the area of a triangle, which is (1/2) * base * height. Since we have the area and the height in terms of the base, we can create an equation:
(1/2) * B * (1.5B) = 147

Simplify that equation: 0.75B^2 = 147

Now, let's divide both sides by 0.75 to solve for B: B^2 = 196

Taking the square root of both sides, we get B = ±14.

Since we're dealing with a triangle, we can't have a negative base length. So, the base of the triangle must be 14 inches.

Now, to find the height, we just need to multiply the base by 1.5: H = 1.5 * 14 = 21 inches.

So, in conclusion, the triangle has a base of 14 inches and a height of 21 inches. Ta-da!

Let's start by setting up the formula for the area of a triangle:

Area of a triangle = (base * height) / 2

We are given that the area is 147 square inches:

147 = (base * height) / 2

It is also given that the height is 1.5 times the base:

height = 1.5 * base

Substituting the height value into the area formula, we get:

147 = (base * (1.5 * base)) / 2
147 = (base^2 * 1.5) / 2
147 = (base^2 * 1.5) / 2
147 = 0.75 * base^2

To solve for the base, we can rearrange the equation:

base^2 = (147 / 0.75)
base^2 = 196
base = sqrt(196)
base = 14 inches

Now, we can find the height using the equation given:

height = 1.5 * base
height = 1.5 * 14
height = 21 inches

Therefore, the base of the triangle is 14 inches and the height is 21 inches.

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

Area = (base * height) / 2

Given that the area of the triangle is 147 square inches, we can substitute this value into the formula:

147 = (base * height) / 2

Since we also know that the height is 1.5 times the base, we can substitute this into the equation as well:

147 = (base * 1.5 * base) / 2

To simplify the equation, we can multiply both sides by 2 to get rid of the denominator:

2 * 147 = base * 1.5 * base

294 = 1.5 * base^2

Next, divide both sides by 1.5 to isolate the base:

294 / 1.5 = base^2

196 = base^2

To find the value of the base, we take the square root of both sides:

√196 = √(base^2)

14 = base

So, the base of the triangle is 14 inches.

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

height = 1.5 * base

height = 1.5 * 14

height = 21

Therefore, the height of the triangle is 21 inches.