The height of a triangle is 2 mm. less than the base. If the area is 60 mm^2, find the height and the base.

A = (1/2) b h

h = b - 2
so
60 = (1/2) b(b-2)

120 = b^2 - 2 b

b^2 - 2 b - 120 = 0

(b-12)(b+10) = 0

b = 12
h = 10

The product of two consecutive integers is 156 what are the two integers

The height of a triangle is 2cm less than the base. If the area is 60 sq. cm, find the height and base of the triangle.

To find the height and base of the triangle, we need to use the formula for the area of a triangle:

Area = (base * height) / 2

We are given that the height is 2 mm less than the base, so let's denote the base as x mm. Therefore, the height can be expressed as (x - 2) mm.

Substituting these values into the area formula, we get:

60 = (x * (x - 2)) / 2

To solve for x, we need to rearrange the equation and solve the resulting quadratic equation.

Step 1: Multiply both sides of the equation by 2 to get rid of the fraction:

120 = x * (x - 2)

Step 2: Distribute x on the right side of the equation:

120 = x^2 - 2x

Step 3: Rearrange the equation to make it equal to 0:

x^2 - 2x - 120 = 0

Step 4: Factorize the quadratic equation or use the quadratic formula to find the values of x:

(x - 12)(x + 10) = 0

The solutions are x = 12 and x = -10. However, since the base of a triangle cannot be negative, we disregard x = -10.

Therefore, the base is x = 12 mm.

To find the height, we substitute the base value into the expression we derived earlier:

Height = x - 2 = 12 - 2 = 10 mm.

So, the height of the triangle is 10 mm and the base is 12 mm.