To determine To calculate: The length and width of the bill, who has a shape of the bill rectangle and which area 112 square centimeters and diagonal 260 centimeters. Explanation Given Information: A country’s currency includes a bill that who’s has an area 112 square centimeters and diagonal 260 centimeters. 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 area of the rectangle A = x × y 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. Area of the bill 112 square centimeters x × y = 112 …… ( 1 ) Diagonal of a bill 260 centimeters x 2 + y 2 = 260 Both side square above equation, x 2 + y 2 = 260 …… ( 2 ) The system of equation becomes x × y = 112 x 2 + y 2 = 260 From equation ( 1 ) x y = 112 y = 112 x Substitute the value of 112 x for y in equation ( 2 ) x 2 + y 2 = 260 x 2 + ( 112 x ) 2 = 260 x 2 + 12544 x 2 = 260 Both side multiply by x 2 x 2 ( x 2 + 12544 x 2 ) = x 2 ( 260 ) x 4 + 12544 = 260 x 2 x 4 − 260 x 2 + 12544 = 0 Let x 2 = t put in above equation t 2 − 260 t + 12544 = 0 This is a quadratic equation to solve by factorization method t 2 − 260 t + 12544 = 0 t 2 − ( 64 + 196 ) t + 12544 = 0 t 2 − 64 t − 196 t + 12544 = 0 t ( t − 64 ) − 196 ( t

Intermediate Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134758992

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 10.4, Problem 45ES

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To calculate: The length and width of the bill, who has a shape of the bill rectangle and which area 112 square centimeters and diagonal 260 centimeters.

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Chapter 10.4, Problem 44ES

Chapter 10.4, Problem 46ES

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Intermediate Algebra For College Students (10th Edition)

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