Question

a triangular shelf has an area of 132 in² with a base of 24 in. use the equation 132 = \frac{1}{2}(24)h to find the height of the shelf.\
options: 66 in, 39 in, 11 in, 4 in

Explanation:

Step1: Simplify the equation

The given equation is \( 132=\frac{1}{2}(24)h \). First, calculate \( \frac{1}{2}\times24 \), which equals \( 12 \). So the equation becomes \( 132 = 12h \).

Step2: Solve for \( h \)

To find \( h \), divide both sides of the equation \( 132 = 12h \) by \( 12 \). So \( h=\frac{132}{12} \). Calculating that, \( 132\div12 = 11 \)? Wait, no, wait. Wait, \( 12\times11 = 132 \)? Wait, no, \( 12\times11 = 132 \)? Wait, no, \( 12\times11 = 132 \)? Wait, no, let's recalculate. Wait, \( 132\div12 \): 1211=132? Wait, 1210=120, 132-120=12, so 10+1=11. Wait, but wait, the options have 11 in? Wait, but let's check the equation again. Wait, the area of a triangle is \( \frac{1}{2}bh \). So \( b = 24 \), area is 132. So \( 132=\frac{1}{2}\times24\times h \). \( \frac{1}{2}\times24 = 12 \), so \( 132 = 12h \). Then \( h = 132\div12 = 11 \). Wait, but the options have 11 in as one of the choices. Wait, but let me check again. Wait, maybe I made a mistake. Wait, 24 times 11 is 264, half of that is 132. Yes, that's correct. So \( h = 11 \) inches. Wait, but the options: 66 in, 39 in, 11 in, 4 in. So the correct answer is 11 in. Wait, but let's go through the steps again.

Wait, step 1: \( 132=\frac{1}{2}(24)h \) => \( 132 = 12h \) (since \( \frac{1}{2}\times24 = 12 \)). Step 2: Divide both sides by 12: \( h = 132\div12 = 11 \). So the height is 11 inches.

Answer:

11 in