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

1 answer

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:

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