Questions: Solve for a Variable (FA24) Question 1, *Quick Check IR2.IR5.23 Part 1 of 2 The area A of a triangle is given by the formula A=1/2 bh, where b is the base of the triangle and h is the height. (a) Solve the formula for b. (b) Find the base of the triangle whose area is 18 square inches and whose height is 9 inches.

Solve for a Variable (FA24)
Question 1, *Quick Check IR2.IR5.23
Part 1 of 2

The area A of a triangle is given by the formula A=1/2 bh, where b is the base of the triangle and h is the height.
(a) Solve the formula for b.
(b) Find the base of the triangle whose area is 18 square inches and whose height is 9 inches.

Transcript text: Solve for a Variable (FA24) Question 1, *Quick Check IR2.IR5.23 Part 1 of 2 The area $A$ of a triangle is given by the formula $A=\frac{1}{2} b h$, where $b$ is the base of the triangle and $h$ is the height. (a) Solve the formula for $b$. (b) Find the base of the triangle whose area is 18 square inches and whose height is 9 inches.

Solution

Solution Steps

Solution Approach

To solve for the base $ b $ in the formula for the area of a triangle $ A = \frac{1}{2} b h $, we need to isolate $ b $ on one side of the equation. This can be done by multiplying both sides by 2 and then dividing by $ h $. For part (b), substitute the given values of area and height into the rearranged formula to find the base.

Step 1: Rearrange the Formula to Solve for $ b $

The area of a triangle is given by the formula:

\[ A = \frac{1}{2} b h \]

To solve for the base $ b $, we need to isolate $ b $ on one side of the equation. Multiply both sides by 2 to eliminate the fraction:

\[ 2A = b h \]

Next, divide both sides by $ h $ to solve for $ b $:

\[ b = \frac{2A}{h} \]

Step 2: Substitute Given Values to Find $ b $

Given that the area $ A = 18 $ square inches and the height $ h = 9 $ inches, substitute these values into the formula:

\[ b = \frac{2 \times 18}{9} \]

Calculate the value:

\[ b = \frac{36}{9} = 4 \]