Area of a Triangle Word Problem

In summary, the problem involves finding the base and height of a triangle given its area and the relationship between its base and height. Using the formula for the area of a triangle, the equation 52=(h^2-5h)/2 is obtained, which can be solved using the quadratic equation. The resulting solutions are h=13 or h=-8, but since h=-8 is extraneous, the height is 8 and the base is 13. While solving quadratic equations is typically an Algebra I topic, there is also the option of guess-and-check in this case. However, using the quadratic equation is the only way to algebraically solve the problem.
  • #1
S.R
81
0

Homework Statement


If the height of a triangle is five centimeters less than the length of its base and if the area of the triangle is 52 cm^2, find the base and the height.

Homework Equations


N/A

The Attempt at a Solution


height = h-5
base = h

A=(bh)/2

52=(h(h-5)/2

52=(h^2-5h)/2

104=h^2-5h

h^2-5h-104=0

(h-13)(h+8)=0

h=13 or h=-8

h=-8 is extraneous; therefore the base is 13 and the height is 8.

This is Grade 9 review and I don't think my teacher would include a problem using the quadratic equation. Is there an easier solution to this problem?
 
Last edited:
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  • #2
S.R said:
This is Grade 9 review and I don't think my teacher would include a problem using the quadratic equation. Is there an easier solution to this problem?
There's always guess-and-check, I suppose...

I'm not sure why you don't think your teacher would include a problem using the quadratic equation. If we assume that Grade 9 = Algebra I (in the US), then sure, solving quadratic equations by factoring is an Algebra I topic.
 
  • #3
eumyang said:
There's always guess-and-check, I suppose...

I'm not sure why you don't think your teacher would include a problem using the quadratic equation. If we assume that Grade 9 = Algebra I (in the US), then sure, solving quadratic equations by factoring is an Algebra I topic.

In Canada, the Grade 9 curriculum involves linear equations.

EDIT: I suppose there is guess-and-check. Using a quadratic equation is the only way to algebraically solve the problem.

/closed
 

FAQ: Area of a Triangle Word Problem

What is the formula for finding the area of a triangle?

The formula for finding the area of a triangle is A = 1/2 * base * height, where A is the area, base is the length of the triangle's base, and height is the perpendicular distance from the base to the opposite vertex.

How do I solve word problems involving the area of a triangle?

To solve word problems involving the area of a triangle, you can follow these steps:

  • Read the problem carefully and identify the given information, such as the base and height of the triangle.
  • Use the formula A = 1/2 * base * height to find the area of the triangle.
  • Check if the units of measurement are the same for all given values and convert if necessary.
  • Answer the question being asked using the calculated area.

What are some real-life applications of finding the area of a triangle?

Finding the area of a triangle is useful in many fields, including architecture, engineering, and construction. For example, architects use the area of a triangle to calculate the amount of materials needed for roofing or flooring. Engineers use it to design structures such as bridges and buildings. Construction workers use it to measure and cut materials for various projects.

Can the area of a triangle be negative?

No, the area of a triangle cannot be negative. It is a measurement of space, and all measurements are positive. If you get a negative value when calculating the area, it means there was an error in your calculations.

Is the area of a triangle affected by the order of the given dimensions?

No, the area of a triangle is not affected by the order of the given dimensions. The formula for finding the area remains the same regardless of the order of the base and height. However, it is important to make sure the base and height values are correctly identified in the given problem.

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