Question

The height of a triangle is half its width. The area of the triangle is 25cm². What are the measures of the base and height

Answer 1

Let the width (base) of the triangle be denoted as \( b \) and the height as \( h \). According to the problem, the height is half of the width, which can be expressed as:

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

The area \( A \) of a triangle is given by the formula:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

Substituting the values for the area and height, we have:

\[
25 = \frac{1}{2} \times b \times \left(\frac{1}{2}b\right)
\]

Simplifying the right side:

\[
25 = \frac{1}{2} \times b \times \frac{1}{2}b = \frac{1}{4} b^2
\]

Now, multiply both sides by 4 to eliminate the fraction:

\[
100 = b^2
\]

Taking the square root of both sides gives:

\[
b = 10 \, \text{cm}
\]

Now, substituting \( b \) back into the equation for height:

\[
h = \frac{1}{2}b = \frac{1}{2} \times 10 = 5 \, \text{cm}
\]

Thus, the measures of the base and height of the triangle are:

\[
\text{Base} = 10 \, \text{cm}
\]
\[
\text{Height} = 5 \, \text{cm}
\]