High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ A skyscraper has a triangular window with an area of 42 square meters. The window's base is 2 meters shorter than twice the height.

Which equation can you use to find [tex]$h$[/tex], the height of the window in meters?

A. [tex]\frac{1}{2}(2h + 2)h = 42[/tex]
B. [tex]\frac{1}{2}(2h)h = 42[/tex]
C. [tex]\frac{1}{2}(2h + 2)(h - 2) = 42[/tex]
D. [tex]\frac{1}{2}(2h - 2)h = 42[/tex]
E. [tex]\frac{1}{2}(h - 2)h = 42[/tex]
F. [tex](2h - 2)h = 42[/tex]

Now, use the equation you picked to find [tex]$h$[/tex].
[tex]$h =$[/tex] \(\square\) meters.

Answer :

To find the height of a triangular window when given certain conditions, let's break it down step-by-step:

1. Identify the Given Data:
- The area of the triangular window is 42 square meters.
- The base of the triangle is 2 meters shorter than twice the height. This can be written as: base = 2 * height - 2.

2. Recall the Formula for the Area of a Triangle:
- The area [tex]\( A \)[/tex] of a triangle is given by the formula:
[tex]\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\][/tex]

3. Set Up the Equation Using the Given Information:
- Substitute the expression for the base into the area formula:
[tex]\[
42 = \frac{1}{2} \times (2h - 2) \times h
\][/tex]

4. Simplify and Arrange the Equation:
- Eliminate the fraction by multiplying the entire equation by 2:
[tex]\[
84 = (2h - 2) \times h
\][/tex]
- Distribute the [tex]\( h \)[/tex] across the terms inside the parenthesis:
[tex]\[
84 = 2h^2 - 2h
\][/tex]

5. Rearrange to Form a Quadratic Equation:
- Bring all terms to one side of the equation to set it to zero:
[tex]\[
2h^2 - 2h - 84 = 0
\][/tex]
- Divide the entire equation by 2 to simplify:
[tex]\[
h^2 - h - 42 = 0
\][/tex]

6. Solve the Quadratic Equation:
- You can solve this quadratic using the quadratic formula, factoring, or other methods, but the height [tex]\( h \)[/tex] that satisfies this equation is:
[tex]\[
h = 7 \text{ meters}
\][/tex]

Therefore, the height of the triangular window is 7 meters.