the area of an isosceles triangle is 12 cm².if one of its equal sides is 5cm find its base
Answers
GIVEN :
Area of an isosceles triangle = 12cm²
The measure of equal sides = 5cm
Then the base of triangle = 2x [ As, we divide the base into two for Pythagoras theorm]
Let the base be x
Area of an isosceles triagle = 1/2 × base × height
According to the problem,
1/2 × 2x × h = 12
xh = 12
xh = 12
h = 12/x
In the triangle ADC,
Base = DC = x cm
Hypotenuse = AC = AB = 5cm
Opposite = AD = 12/x
From Pythagoras theorm,
AC² = AD² + BC²
5² = (12/x)² + x²
25 = 144/x² + x²
After the LCM,
x⁴ + 25x² - 144 = 0
Split the middle term,
x⁴ - 16x² - 9x² - 144 = 0
x²( x² - 16) - 9(x² - 16) = 0
x² - 16 = 0 ; x² - 9 = 0
x² = 16 ; x² = 9
x = √16 ; x = √9
x = 4 ; x = 3
We got two solutions x = 3 & 4.
Therefore, the whole base will be 3 × 2 = 6 or 4 × 2 = 8
Therefore, the whole base will be 3 × 2 = 6 or 4 × 2 = 8Then the height will be (12/3 & 12/4 ) = 3 or 4.
Answer:
6 or 8
Step-by-step explanation: