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
46 cm
60 cm

Explanation:

Step1: Set up variables

Let the height of the triangle be \( h \) cm. Then the base \( b = 5h \) cm. The area formula for a triangle is \( A=\frac{1}{2}bh \).

Step2: Substitute values into the formula

Given \( A = 1440\) \(cm^{2}\), substitute \( b = 5h \) into \( A=\frac{1}{2}bh \). We get \( 1440=\frac{1}{2}(5h)h \).
Simplify the equation: \( 1440=\frac{5h^{2}}{2} \).

Step3: Solve for \( h^{2} \)

Multiply both sides by \( 2 \): \( 1440\times2 = 5h^{2} \), so \( 2880 = 5h^{2} \).
Then divide both sides by \( 5 \): \( h^{2}=\frac{2880}{5}=576 \).

Step4: Solve for \( h \)

Take the square - root of both sides: \( h=\sqrt{576} \). Since \( h>0 \) (height cannot be negative), \( h = 24 \) cm.

Answer:

24 cm