Question

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

Answer 1

The height of the triangle is found by using the area formula of a triangle and setting up a quadratic equation based on the given information. We solve the equation to find the base and then subtract 6 cm to get the height, which is 6 cm.

Step-by-step explanation:

To find the height of a triangle when given the area and the relationship between the base and the height, we can use the area formula of a triangle which is Area = 1/2 × base × height. In this problem, we know that the area is 36 cm2, and the height is 6 cm less than the base. So, if we let x represent the base, then the height is x - 6 cm.

Using the area of a triangle formula, we set up the equation: 1/2 × x × (x - 6) = 36. To solve for x, we first multiply through by 2 to get rid of the fraction:

x(x - 6) = 72

We then expand this to get a quadratic equation:

x2 - 6x - 72 = 0

Solving this quadratic equation by factoring, we find that x = 12 is a possible solution. Therefore, the height is x - 6 = 12 - 6 = 6 cm, which is option B.

Answer 2

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