Step 1: Make a note of the known and unknown measurements

Step 2: Represents the given relation between height and base through variables.

NOTE: height (h) is 4 units shorter than its base

h = b - 4

Step 3: Set up a formula of area of isosceles triangle to write

FORMULAS:

Area of an isosceles triangle = \frac{1}{2} b*h

Where b - base and h - height (altitude)

h (Altitude) = \sqrt{a^2 - \frac{b^2}{4}}

Step 4: Substitute the known values in the area formula.

EXAMPLE: Area of an isosceles triangle = \frac{1}{2} b*h

30 = [math]\frac{1}{2}\ \left[b\ \left(b\ -\ 4\right)\right]\ [/math]

Step 5: Simplify the equation to find the unknown value (base)

EXAMPLE : 60 = b^2 - 4b

b^2-4b-60=0

Solve the quadratic equation

b^2 - 10b + 6b - 60 = 0

b(b - 10) + 6 (b - 10) = 0

(b - 10)(b + 6) = 0

Solutions to the equation: b = 10 and b = - 6

b is a length and therefore is positive b = 10

Step 6: Find the height of the triangle by plugging the base values in the relation

EXAMPLE; h = b -4

h = 10 - 4 = 6

Step 7: Set up a formula to calculate the lateral side of an isosceles triangle.

NOTE: Isosceles triangle is a combination of two right triangle.

Pythagoras theorem

FORMULA: (lateral\ side)^2=(height)^2+\left(\frac{base}{2}\right)^2

Step 8: Find the lateral side of an isosceles triangle.

EXAMPLE: (lateral\ side)^2=6^2+(\frac{10}{2})^2

lateral\ side=\sqrt{36\ +\ 25}

lateral\ side=\sqrt{61}