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Math  /  Geometry

QuestionGot It? 3. What is the height of a triangle that has an area of 24in224 \mathrm{in}^{2} and a base with a length of 8 in.?

Studdy Solution

STEP 1

What is this asking? We need to find how tall a triangle is if its area is 24 square inches and its base is 8 inches long. Watch out! Don't mix up the area and the height!
The area is how much space the triangle covers, while the height is how tall it stands.

STEP 2

1. Recall the triangle area formula.
2. Plug in what we know.
3. Solve for the height.

STEP 3

Alright, remember how to find the area of a triangle?
It's 12\frac{1}{2} times the base times the height!
We can write that as: Area=12⋅base⋅height \text{Area} = \frac{1}{2} \cdot \text{base} \cdot \text{height}

STEP 4

We know the **area** is 24 in2\text{24 in}^2 and the **base** is 8 in\text{8 in}.
Let's **plug those values** into our formula: 24=12⋅8⋅height 24 = \frac{1}{2} \cdot 8 \cdot \text{height}

STEP 5

Now, let's **simplify**!
What's 12\frac{1}{2} times 8?
That's 4!
So, we have: 24=4⋅height 24 = 4 \cdot \text{height}

STEP 6

To **isolate** the height, we need to divide both sides of the equation by 4.
Dividing 24 by 4 gives us 6, and dividing 4 by 4 gives us 1.
Remember, we're dividing to one! 244=4⋅height4 \frac{24}{4} = \frac{4 \cdot \text{height}}{4} 6=height 6 = \text{height}

STEP 7

So, the **height** of the triangle is 6 in\text{6 in}!

STEP 8

The height of the triangle is 6 in\text{6 in}.

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