The area of a triangle is 124 square units. What would its new area be if its base was half as long, and its height was three times as long?

I have no idea what I should use or do to solve this question. I only got to the point in where the new area is technically 1/2 (b/2)(3h). Please help! Thanks!

b h / 2 = 124

1/2 (b/2)(3h) = 3/2 (b h / 2) = 3/2 (124)

Oh! That actually makes a lot of sense. Thanks R_scott!

Well, let's put on our mathematician clown wig and solve this problem with a touch of humor!

First, we need to find the area of the original triangle. Since we already know the area is 124 square units, let's call the base of the triangle 'b' and the height 'h'.

Now, to find the new area, we're told that the base is going to be half as long and the height is going to be three times as long. So, the new base will be 'b/2' and the new height will be '3h'.

To find the new area, we simply plug these values into the formula for the area of a triangle: Area = (1/2) * base * height.

So, the new area will be:

New Area = (1/2) * (b/2) * (3h)

Now, let's put this equation on a unicycle and make it work for us!

New Area = (1/2) * (b/2) * (3h)

Simplifying this equation, we get:

New Area = (3/4) * b * 3h

Multiplying it out further, we get:

New Area = (9/4)bh

So, in clown terms, if the initial area of the triangle was 124 square units, the new area will be (9/4) times the original area.

Does that make you smile? I hope so!

To find the new area of a triangle when its base is half as long and its height is three times as long, you can use the formula for the area of a triangle:

Area = (1/2)(base)(height)

Let's assume the original base and height of the triangle are represented by 'b' and 'h' respectively. So, the original area, A, can be calculated as:

A = (1/2)(b)(h) ------ Equation 1

Now, according to the question, the new base is half as long (b/2) and the new height is three times as long (3h).

The new area, A', can be calculated using the same formula:

A' = (1/2)(b/2)(3h) ------ Equation 2

To find the relationship between the original area (A) and new area (A'), we can divide Equation 2 by Equation 1:

A' / A = [(1/2)(b/2)(3h)] / [(1/2)(b)(h)]

Simplifying the equation:

A' / A = (1/2)*(b/2)*(3h) / (1/2)*(b)*(h)
= (1/4)*(3h)*(b) / (1)*(b)*(h)
= 3/4

Therefore, the new area, A', is 3/4 times the original area, A.

To find the actual value of the new area, you need to multiply the original area by 3/4:

New Area, A' = (3/4) * A

Substituting the given original area of 124 square units:

New Area, A' = (3/4) * 124
= 93 square units

Hence, the new area of the triangle would be 93 square units if its base was half as long, and its height was three times as long.

To find the new area of the triangle, you can use the formula for the area of a triangle, which is given by:

Area = (1/2) * base * height

Given that the original area of the triangle is 124 square units, let's solve for the original base and height. Rearranging the formula, we have:

124 = (1/2) * base * height

Now, let's solve for the base and height:

base * height = 248

To find the new area, we need to know the new base and height. Given that the new base is half as long and the new height is three times as long as the original base and height, we can express this as:

new base = (1/2) * original base
new height = 3 * original height

Let's substitute these values into the equation:

new base * new height = (1/2) * original base * 3 * original height

By substituting the values from the original equation, we have:

new base * new height = (1/2) * base * height * 3

Simplifying further, we get:

new base * new height = 3/2 * base * height

Given that the original base * height is 248 (from earlier calculations), we can substitute it into the equation:

new base * new height = 3/2 * 248

To find the new area, we substitute the equation for the area of a triangle, using the new base and new height:

New Area = (1/2) * new base * new height = (1/2) * (3/2) * 248

Simplifying further:

New Area = (1/2) * 372 = 186 square units

Therefore, the new area of the triangle would be 186 square units if its base was half as long and its height was three times as long.