Question

2 - 53. the area of the triangle at right is 25 square feet. determine the value of h. then calculate the perimeter of the entire triangle. show all work. homework help

Explanation:

Step1: Find the value of \( h \)

The area formula of a triangle is \( A=\frac{1}{2}\times base\times height \). Here, \( A = 25\) square feet, base \( b=5 \), and height \( h \).
Substitute into the formula: \( 25=\frac{1}{2}\times5\times h \).
Solve for \( h \):

$$
LATEXBLOCK0
$$

Step2: Calculate the length of the hypotenuse

Use the Pythagorean theorem \( c=\sqrt{a^{2}+b^{2}} \) for the right - angled sub - triangle with \( a = 6\) and \( b = 10\).

$$
LATEXBLOCK1
$$

Step3: Calculate the perimeter \( P \)

The perimeter of the triangle \( P=5 + 6+2\sqrt{34}\).

$$
LATEXBLOCK2
$$

Answer:

The value of \( h = 10\) feet. The perimeter of the triangle is approximately \( 22.66\) feet.