Find X in Right Triangle: Area 18.5 and Height 10 Units

Question

Calculate X using the data in the figure below.

A=18.5A=18.5A=18.5XXX101010AAABBBCCC

Video Solution

Solution Steps

00:00 Determine the value of X
00:03 Apply the formula for calculating the area of a triangle
00:06 (base X height) divided by 2
00:09 Substitute in the relevant values according to the given data and proceed to solve for X
00:13 Isolate X
00:17 This is the solution

Step-by-Step Solution

To find the missing side X X of the triangle:

  • Step 1: Identify the given values: area A=18.5 A = 18.5 and height h=10 h = 10 .
  • Step 2: Use the area formula for a triangle: A=12×base×height A = \frac{1}{2} \times \text{base} \times \text{height} .
  • Step 3: Plug in the known values into the formula:
    18.5=12×X×10 18.5 = \frac{1}{2} \times X \times 10 .
  • Step 4: Simplify and solve for X X :
    18.5=5×X 18.5 = 5 \times X
    Divide both sides by 5 to isolate X X :
    X=18.55 X = \frac{18.5}{5} .
  • Step 5: Calculate X X :
    X=3.7 X = 3.7 .

Therefore, the missing side X X is 3.7 3.7 .

Answer

3.7