In Exercises 8 to 10, use the properties of rectangles to solve each problem. Rectangle ABCD is shown in the figure.
Exercises 8 – 10
Given: | AB = x + y and BC = x + 2y, and CD = 2x – y – 1, and DA = 3x – 3y + 1 | |
Find: | x and y |
To find:
x and y of the given rectangle.
The basic property of rectangle:
1) All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other).
2) All angles are right angles by definition.
3) The diagonals are congruent.
Calculation:
Given: AB = x + y and BC = x + 2y, and CD = 2x â€“ y â€“ 1, and DA = 3x â€“ 3y + 1
Consider the rectangle.
Now we have to find x and y of the given rectangle.
To find x and y:
From the property, opposite sides are congruent in rectangle.
So, AB = CD
BC = DA
Now we have to solve (1) and (2).
By solving (1), we get
By solving (2), we get
Calculus: Early Transcendental Functions
Mathematical Excursions (MindTap Course List)
Intermediate Algebra
Applied Calculus
Elementary Technical Mathematics
Finite Mathematics
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendentals
Essentials Of Statistics
Probability and Statistics for Engineering and the Sciences
Multivariable Calculus
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus: An Applied Approach (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Understanding Basic Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus
Mathematical Applications for the Management, Life, and Social Sciences
Trigonometry (MindTap Course List)
Elements Of Modern Algebra
Contemporary Mathematics for Business & Consumers
Calculus of a Single Variable
Single Variable Calculus: Early Transcendentals
Elementary Geometry for College Students
Calculus: Early Transcendental Functions (MindTap Course List)
Finite Mathematics for the Managerial, Life, and Social Sciences
Study Guide for Stewart's Multivariable Calculus, 8th
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th