How Do You Solve a Pre Calculus Problem with Congruent Sides and Diagonals?

In summary, the problem is to find the value of x in a quadrilateral with two pairs of congruent sides and a longer diagonal of length 6, such that the area of the shaded region is 40% of the area of the unshaded region. The equation x=0.4(6-x) is used to solve for x. The final answer is x=1.71.
  • #1
shawonna23
146
0
[SOLVED] Pre Calculus Homework Problem...Help!

1. Homework Statement

A quadrilateral has two pairs of congruent sides and a longer diagonal of length of 6, as shown. For what value of x will the area of the shaded region be 40% of the area of the unshaded region?


2. Homework Equations

x=.40(6-x)

3. The Attempt at a Solution

x=1.71
 

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  • #2
the area of shaded region is S1 = x*a and of unshaded S2 = (6-x)a. You also know that S1/S2 = 0.4 . Now just solve the equation for x.
 
  • #3
Pre Cal Hwk Problem: Answer

x(a)/(6-x)(a)= 0.4
The a's cancel out...so that leaves me with: x/(6-x)=0.4 x=2.4/1.4 x=1.71

Is my work correct?
 
  • #4
It looks fine. The important thing is to realize where the areas came from.
 
  • #5
Thanks for the help!
 

Related to How Do You Solve a Pre Calculus Problem with Congruent Sides and Diagonals?

What is Pre Calculus?

Pre Calculus is a branch of mathematics that prepares students for the study of Calculus. It includes topics such as functions, algebraic equations, geometry, and trigonometry.

Why is Pre Calculus important?

Pre Calculus is important because it serves as a foundation for the study of Calculus, which is a crucial subject for students pursuing careers in science, engineering, and mathematics. It also helps develop critical thinking and problem-solving skills.

What are some common topics covered in Pre Calculus?

Some common topics covered in Pre Calculus include functions, limits, derivatives, integrals, and trigonometry. Other topics may include logarithms, exponential functions, and conic sections.

How can I improve my understanding of Pre Calculus?

To improve your understanding of Pre Calculus, it is important to practice regularly and seek help from teachers or tutors when needed. You can also use online resources such as videos, practice problems, and interactive tutorials to supplement your learning.

How can I solve Pre Calculus homework problems more efficiently?

To solve Pre Calculus homework problems more efficiently, it is helpful to break down the problem into smaller steps and make sure you understand the concepts involved. It is also important to check your work and seek help if you get stuck on a particular problem.

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