Question

question 1 (1 point)
the area of the triangle below is 210a², find
the height

height =
(leave your answer as a simplified fraction)

Explanation:

Step1: Recall the area formula of a triangle

The area formula of a triangle is \(A=\frac{1}{2}\times base\times height\). Let the base \(b = 30\) and the area \(A=210\), and the height be \(h\). Then the formula becomes \(210=\frac{1}{2}\times30\times h\).

Step2: Simplify the equation

First, simplify \(\frac{1}{2}\times30\) in the equation \(210=\frac{1}{2}\times30\times h\). \(\frac{1}{2}\times30 = 15\), so the equation is \(210 = 15h\).

Step3: Solve for \(h\)

To find \(h\), divide both sides of the equation \(210=15h\) by \(15\). \(h=\frac{210}{15}\). Simplify \(\frac{210}{15}\) by dividing both the numerator and the denominator by their greatest - common divisor, which is \(15\). \(\frac{210\div15}{15\div15}=14\).

Answer:

\(14\)