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bh/2 = 27
(h+3)h/2 = 27
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The base of a triangle is 3 cm greater than the height. The area is 27 cm squared. Find the height and base of the triangle.
Steve
answered7 years ago
Step-by-Step Bot
answered1 year ago
Let's represent the height of the triangle as 'h' cm.
According to the given information, the base is 3 cm greater than the height. Therefore, the base of the triangle can be represented as 'h + 3' cm.
The area of a triangle can be calculated using the formula:
Area = (1/2) * base * height
Substituting the given values into the formula, we have:
27 = (1/2) * (h + 3) * h
To solve for the height, we need to rearrange the equation and solve for 'h':
27 = (1/2) * (h^2 + 3h)
Multiplying both sides by 2 to eliminate the fraction:
54 = h^2 + 3h
Rearranging the equation and setting it equal to zero:
h^2 + 3h - 54 = 0
We can now solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's solve it by factoring:
(h + 9)(h - 6) = 0
Setting each factor equal to zero:
h + 9 = 0 or h - 6 = 0
Solving for 'h' in each case:
h = -9 or h = 6
Since the height of a triangle cannot be negative, we can discard h = -9.
Therefore, the height of the triangle is 6 cm.
Substituting this value back into one of the earlier equations for the base:
base = height + 3 = 6 + 3 = 9 cm
So, the height of the triangle is 6 cm and the base is 9 cm.
Explain Bot
answered1 year ago
To find the height and base of the triangle, we can use the formula for the area of a triangle:
Area = (base * height) / 2
Given that the area is 27 cm² and the base is 3 cm greater than the height, we can set up the following equation:
27 = (height * (height + 3)) / 2
Let's solve this equation step-by-step to find the values of the height and base.
Step 1: Multiply both sides of the equation by 2 to eliminate the fraction:
27 * 2 = height * (height + 3)
Step 2: Simplify both sides of the equation:
54 = height^2 + 3height
Step 3: Rearrange the equation:
height^2 + 3height - 54 = 0
Step 4: Factorize the quadratic equation:
(height - 6)(height + 9) = 0
Now we have two possible solutions for the height:
1. height - 6 = 0 --> height = 6
2. height + 9 = 0 --> height = -9
Since the height of a triangle cannot be negative, we discard the second solution. Therefore, the height of the triangle is 6 cm.
To find the base, we use the given information that the base is 3 cm greater than the height. So, the base is:
base = height + 3 = 6 + 3 = 9 cm
Therefore, the height of the triangle is 6 cm and the base is 9 cm.