Solved on Dec 21, 2023

Find the height $h$ of a triangle given its area $A$ and base $b$ , where $A = \frac{1}{2} b h$ . Choose the correct formula for $h$ .

STEP 1

Assumptions
1. The formula for the area of a triangle is $A = \frac{1}{2} b h$
2. We need to solve for $h$

STEP 2

To solve for $h$ , we need to isolate $h$ on one side of the equation. We start by multiplying both sides of the equation by 2 to eliminate the fraction.
$2 \cdot A = 2 \cdot \frac{1}{2} b h$

STEP 3

The 2 on the right side of the equation cancels out the $\frac{1}{2}$ , simplifying the equation to:
$2A = b h$

STEP 4

Now, we need to isolate $h$ by dividing both sides of the equation by $b$ .
$\frac{2A}{b} = \frac{b h}{b}$

STEP 5

The $b$ on the right side of the equation cancels out, leaving $h$ isolated:
$h = \frac{2A}{b}$

STEP 6

We have now solved for $h$ in terms of $A$ and $b$ , and the correct answer is:
$h = \frac{2A}{b}$
This corresponds to option D) $h = \frac{2A}{b}$ .

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Find the height $h$ of a triangle given its area $A$ and base $b$ , where $A = \frac{1}{2} b h$ . Choose the correct formula for $h$ .

STEP 1

Assumptions
1. The formula for the area of a triangle is $A = \frac{1}{2} b h$
2. We need to solve for $h$

STEP 2

To solve for $h$ , we need to isolate $h$ on one side of the equation. We start by multiplying both sides of the equation by 2 to eliminate the fraction.
$2 \cdot A = 2 \cdot \frac{1}{2} b h$

STEP 3

The 2 on the right side of the equation cancels out the $\frac{1}{2}$ , simplifying the equation to:
$2A = b h$

STEP 4

Now, we need to isolate $h$ by dividing both sides of the equation by $b$ .
$\frac{2A}{b} = \frac{b h}{b}$

STEP 5

The $b$ on the right side of the equation cancels out, leaving $h$ isolated:
$h = \frac{2A}{b}$

STEP 6

We have now solved for $h$ in terms of $A$ and $b$ , and the correct answer is:
$h = \frac{2A}{b}$
This corresponds to option D) $h = \frac{2A}{b}$ .

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Find the height hhh of a triangle given its area AAA and base bbb, where A=12bhA = \frac{1}{2} b hA=21​bh. Choose the correct formula for hhh.

STEP 1

Assumptions1. The formula for the area of a triangle is A=12bh A = \frac{1}{2} b h A=21​bh2. We need to solve for h h h

STEP 2

To solve for h h h, we need to isolate h h h on one side of the equation. We start by multiplying both sides of the equation by 2 to eliminate the fraction.2⋅A=2⋅12bh 2 \cdot A = 2 \cdot \frac{1}{2} b h 2⋅A=2⋅21​bh

STEP 3

The 2 on the right side of the equation cancels out the 12\frac{1}{2}21​, simplifying the equation to:2A=bh 2A = b h 2A=bh

STEP 4

Now, we need to isolate h h h by dividing both sides of the equation by b b b.2Ab=bhb \frac{2A}{b} = \frac{b h}{b} b2A​=bbh​

STEP 5

The b b b on the right side of the equation cancels out, leaving h h h isolated:h=2Ab h = \frac{2A}{b} h=b2A​

STEP 6

We have now solved for h h h in terms of A A A and b b b, and the correct answer is:h=2Ab h = \frac{2A}{b} h=b2A​This corresponds to option D) h=2Ab h = \frac{2A}{b} h=b2A​.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the height $h$ of a triangle given its area $A$ and base $b$ , where $A = \frac{1}{2} b h$ . Choose the correct formula for $h$ .

Assumptions
1. The formula for the area of a triangle is $A = \frac{1}{2} b h$
2. We need to solve for $h$

To solve for $h$ , we need to isolate $h$ on one side of the equation. We start by multiplying both sides of the equation by 2 to eliminate the fraction.
$2 \cdot A = 2 \cdot \frac{1}{2} b h$

The 2 on the right side of the equation cancels out the $\frac{1}{2}$ , simplifying the equation to:
$2A = b h$

Now, we need to isolate $h$ by dividing both sides of the equation by $b$ .
$\frac{2A}{b} = \frac{b h}{b}$

The $b$ on the right side of the equation cancels out, leaving $h$ isolated:
$h = \frac{2A}{b}$

We have now solved for $h$ in terms of $A$ and $b$ , and the correct answer is:
$h = \frac{2A}{b}$
This corresponds to option D) $h = \frac{2A}{b}$ .