The dimensions of a rectangular parcel.

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 10T
To determine

The dimensions of a rectangular parcel.

Expert Solution

The dimensions of the parcel is 50ft by 120ft .

Explanation of Solution

Given:

The rectangular parcel is 70ft longer than its width and the diagonal between opposite corner is 130ft .

Calculation:

Let the width is w, length is l and diagonal is d of the parcel.

The given condition states that the length of parcel is 70ft longer than its width that is,

l=w+70

Use Pythagoras theorem for w, l, and d,

w2+l2=d2

Substitute 130 for d and w+70 for l in the above equation and solve for width of parcel,

w2+(w+70)2=(130)2w2+w2+140w+4900=169002w2+140w12000=0w2+70w6000=0

Further, solve above equation for value of w,

w2+120w50w6000=0w(w+120)50(w+120)=0(w50)(w+120)=0w=50,120

The width of land must be a positive number because dimensions cannot be measure in negative number so conclude that w=50ft .

Substitute 50 for w into l=w+70 and solve for length of parcel,

l=50+70l=120

Thus, the dimensions of the parcel is 50ft by 120ft .

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