The base of a triangle is 7cm greater than the height. the area is 60cm^2. find the height and the lenght of the base.

Area = .5(base * height)

Let h = height, and b = base

h + 7 = b

60 = .5(h +7)h

120 = (h + 7)h

h = 8

The height of a triangle is 77 centimeters greater than the base. The area of the triangle is 114114 square centimeters. Find the length of the base and the height of the triangle.

Let's assume the height of the triangle is 'h' cm.

According to the given information, the base of the triangle is 7 cm greater than the height. Therefore, the length of the base is 'h + 7' cm.

The formula to calculate the area of a triangle is given as Area = (base * height) / 2.

Given that the area of the triangle is 60 cm^2, we can write the equation as:

60 = (h + 7) * h / 2

Now, let's solve for 'h':

Multiply both sides of the equation by 2 to eliminate the fraction:

120 = (h + 7) * h

Expanding the equation:

120 = h^2 + 7h

Rearrange the equation to get a quadratic equation:

h^2 + 7h - 120 = 0

Now, we can factorize or use the quadratic formula to solve for 'h'. Let's use the quadratic formula:

h = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 7, and c = -120:

h = (-7 ± √(7^2 - 4*1*(-120))) / (2*1)

Solving this equation gives us two possible values for 'h'. Let's calculate both:

h = (-7 ± √(49 + 480)) / 2
h = (-7 ± √529) / 2
h = (-7 ± 23) / 2

We obtain two possible values for 'h': h = (-7 + 23) / 2 = 8 cm, and h = (-7 - 23) / 2 = -15 cm.

Since a negative height doesn't make sense in this context, we can discard the negative value and conclude that the height of the triangle is 8 cm.

Now, we can find the length of the base by adding 7 cm to the height:

Length of base = 8 cm + 7 cm = 15 cm.

Therefore, the height of the triangle is 8 cm, and the length of the base is 15 cm.

To solve this problem, we can use the formula for the area of a triangle: Area = (base * height) / 2.

From the given information, we know that the area is 60 cm^2. Let's call the height of the triangle 'h' cm.

Now, according to the question, the base of the triangle is 7 cm greater than the height. So, the base can be expressed as (h + 7) cm.

Substituting these values into the formula for the area, we get:
60 = ((h + 7) * h) / 2

To solve this equation, we can start by simplifying it:
120 = h^2 + 7h

Next, we need to rearrange the equation in standard quadratic form:
h^2 + 7h - 120 = 0

At this point, we can either factorize the equation or solve it using the quadratic formula. Let's use the quadratic formula:

The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a

In our equation, the coefficient of h^2 (a) is 1, the coefficient of h (b) is 7, and the constant term (c) is -120.

Plugging these values into the quadratic formula, we get:
h = (-7 ± √(7^2 - 4(1)(-120))) / (2(1))

Simplifying further:
h = (-7 ± √(49 + 480)) / 2
h = (-7 ± √(529)) / 2
h = (-7 ± 23) / 2

Now, we have two potential solutions for the height:
1. h = (-7 + 23) / 2 = 16 / 2 = 8 cm
2. h = (-7 - 23) / 2 = -30 / 2 = -15 cm

Since a negative height doesn't make sense in this context, we can discard the second solution.

Therefore, the height of the triangle is 8 cm.

To find the length of the base, we can substitute this value back into the equation for the base:
base = h + 7 = 8 + 7 = 15 cm

Therefore, the height of the triangle is 8 cm and the length of the base is 15 cm.