Mathematics: The area of a triangle is 36 cm2. The height of the triangle is 6 cm less than the base. What is the height of the triangle? A) 4 cm B) 6 cm C) 8 cm D) 12 cm

The area of a triangle is 36 cm2. The height

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20.01.2022

Height of triangle = 6 cm

Step-by-step explanation:

Let,

Height of triangle = h

Base of triangle = b

Given Data:

Area of triangle = A = $36 cm^{2}$

According to given condition:

h = b - 6

To find out:

Height of triangle = h = ?

Formula:

Area of triangle = A = (b × h)/2

Solution:

Area of triangle = A = (b × h)/2

36 = (b × h)/2

36 × 2 = b × (b - 6 ) ∴h = b - 6

$72 = b^{2} - 6b$

$b^{2} - 6b - 72 = 0$

$b^{2} - 12b + 6b - 72 = 0$

$(b^{2} - 12b) +( 6b - 72) = 0$

b(b - 12) + 6( b - 12) = 0

(b - 12)( b + 6) = 0

b- 12 = 0 or b + 6 = 0

b = 12 or b = -6

As base value is always positive, so

Base of triangle = b = 12 cm

h = b - 6

h = 12 - 6

Height of triangle = 6 cm

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