Question

1. the height of a triangle is 6 cm and the area of the triangle is 24 cm². what is the length of the base of the triangle? answer with supporting work.

Explanation:

Step1: Recall the area formula of a triangle

The area formula of a triangle is \( A=\frac{1}{2}\times b\times h \), where \( A \) is the area, \( b \) is the base, and \( h \) is the height. We know \( A = 24\space cm^2 \) and \( h=6\space cm \), and we need to find \( b \).

Step2: Rearrange the formula to solve for \( b \)

From \( A=\frac{1}{2}\times b\times h \), we can multiply both sides by 2 to get \( 2A = b\times h \), then divide both sides by \( h \) to obtain \( b=\frac{2A}{h} \).

Step3: Substitute the known values into the formula

Substitute \( A = 24\space cm^2 \) and \( h = 6\space cm \) into \( b=\frac{2A}{h} \). So \( b=\frac{2\times24}{6} \).

Step4: Calculate the value of \( b \)

First, calculate the numerator: \( 2\times24 = 48 \). Then divide by the denominator: \( \frac{48}{6}=8 \).

Answer:

The length of the base of the triangle is \( 8\space cm \).