To determine To calculate: The dimension of the plywood which has a rectangular piece. When he measure the diagonal it measures 34 inches. When he cut the plywood along the diagonal, the perimeter of each triangle formed is 80 inches. Explanation Given Information: A rectangular piece of a plywood has a diagonal 34 inches and the perimeter of the triangle is 80 inches. Formula used: Step1: Formulate the given information Step2: Translate the provided statement in mathematical equation Step3: Solve the mathematical equation that are obtain in step 2 Step3: Verify the solution Step5: Write the required answer The zero-factor property states that if m ⋅ n = 0 , then either m = 0 or n = 0 or both m = 0 and n = 0 The perimeter of the triangle P = x + y + d . The diagonal of the rectangle D = x 2 + y 2 Where, x is the length of the rectangle and y is the width of the rectangle and d is the length of the diagonal. Calculation: Consider a length and width of the rectangle are x and y , Diagonal of the ice rink 34 inches. x 2 + y 2 = 34 Both side square, x 2 + y 2 = 34 2 …… (1) Perimeter of the triangle 80 inches x + y + 34 = 80 x + y = 46 …… (2) The system of equation becomes x 2 + y 2 = 1156 x + y = 46 From equation ( 2 ) x + y = 46 y = 46 − x Substitute the value of 46 − x for y in equation (1) x 2 + y 2 = 1156 x 2 + ( 46 − y ) 2 = 1156 x 2 + ( 2116 + y 2 − 92 x ) = 1156 2 x 2 − 92 x + 960 = 0 Divided by 2 above equation x 2 − 46 x + 480 = 0 x 2 − ( 16 + 30 ) x + 480 = 0 x 2 − 16 x − 30 x + 480 = 0 ( x − 16

Intermediate Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134758992

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 10.4, Problem 47ES

To determine

To calculate: The dimension of the plywood which has a rectangular piece. When he measure the diagonal it measures 34 inches. When he cut the plywood along the diagonal, the perimeter of each triangle formed is 80 inches.

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Chapter 10.4, Problem 46ES

Chapter 10.4, Problem 48ES

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Intermediate Algebra For College Students (10th Edition)

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