Question

the area of a triangular garden is 16 ft². the base is twice the height. find the base and height of the triangle.
part 1 of 2
the base is
part 2 of 2
the height is

Explanation:

Step1: Set up variables

Let the height of the triangle be \( h \) ft. Then the base \( b = 2h \) ft. The area formula for a triangle is \( A=\frac{1}{2}bh \). Substitute \( b = 2h \) and \( A = 16 \) into the formula: \( 16=\frac{1}{2}(2h)h \).

Step2: Simplify the equation

Simplify \( 16=\frac{1}{2}(2h)h \). The \( \frac{1}{2}\times2 \) cancels out, giving \( 16=h^{2} \).

Step3: Solve for \( h \)

Take the square root of both sides. Since height cannot be negative, \( h=\sqrt{16}=4 \) ft.

Step4: Find the base

Since \( b = 2h \), substitute \( h = 4 \). Then \( b=2\times4 = 8 \) ft.

Answer:

The base is \( 8 \) ft.
The height is \( 4 \) ft.