Calculate the Median Length AD in an Isosceles Triangle with Area 60 cm²

Question

Triangle ABC is isosceles.

AD is the median of the BC.
ABC has an area of 60 cm².
BD = 5

Calculate the length AD.

00:00 Calculate AD

00:04 We'll identify the sides and lines according to the given data

00:11 Equal sides according to the given data (isosceles)

00:15 Perpendicular according to the given data

00:24 In an isosceles triangle, the height is also a median

00:39 The whole side equals the sum of its parts

00:49 Apply the formula for calculating the triangle's area

00:55 (height x base) divided by 2

01:01 Substitute in the relevant values and proceed to solve for AD

01:08 Multiply by denominators to eliminate fractions

01:16 Isolate AD

01:33 This is the solution

To calculate the length of the median AD, follow these steps:

Step 1: Calculate the length of the base BC. Since AD is the median, and BD = DC = 5 cm, the total length is $BC = 5 + 5 = 10 \, \text{cm}$ .
Step 2: Use the area formula for triangle ABC, where $S = \frac{1}{2} \times BC \times AD$ . Given $S = 60 \, \text{cm}^2$ , substitute the known values: $60 = \frac{1}{2} \times 10 \times AD$ .
Step 3: Solve for $AD$ by simplifying: $60 = 5 \times AD$ implies $AD = \frac{60}{5} = 12 \, \text{cm}$ .

Therefore, the length of the median AD is $12 \, \text{cm}$ .

12 cm