Question

the area of a triangle is 1,440 cm². the base of the triangle is 5 times the height. what is the height of the triangle? 12 cm 24 cm 48 cm 60 cm

Explanation:

Step1: Recall triangle - area formula

The area formula of a triangle is $A=\frac{1}{2}bh$, where $A$ is the area, $b$ is the base, and $h$ is the height. Given that $b = 5h$ and $A=1440$ $cm^{2}$.

Step2: Substitute $b = 5h$ into the area formula

Substitute $b = 5h$ into $A=\frac{1}{2}bh$, we get $A=\frac{1}{2}(5h)h=\frac{5}{2}h^{2}$.

Step3: Solve for $h$

Since $A = 1440$ $cm^{2}$, we have the equation $\frac{5}{2}h^{2}=1440$. Multiply both sides of the equation by $\frac{2}{5}$: $h^{2}=\frac{2\times1440}{5}=576$. Then take the square - root of both sides. Since $h>0$ (height cannot be negative), $h = \sqrt{576}=24$ $cm$.

Answer:

24 cm