SOLUTION: A)If the width of a rectangle is 1 inch less than its length and the diagonal is 1 inch longer than its length, find the length and the width. B)What is the length of the diagon

Algebra ->  Rectangles -> SOLUTION: A)If the width of a rectangle is 1 inch less than its length and the diagonal is 1 inch longer than its length, find the length and the width. B)What is the length of the diagon      Log On


   

Question 195594: A)If the width of a rectangle is 1 inch less than its length and the diagonal is 1 inch longer than its length, find the length and the width.
B)What is the length of the diagonal of a rectangular bill board with sides of lengths 5 ft and 12 ft.
Answer by MathTherapy(10552) About Me  (Show Source):
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A.
Let the length of the rectangle be L
Then the width of the rectangle is L – 1, since width is 1” less that its length
Also, since its diagonal is 1” longer than its length, then its diagonal = L + 1
Using Pythagorean, we get:

L%5E2%2B%28L-1%29%5E2+=+%28L%2B1%29%5E2

L%5E2%2B%28L-1%29%28L-1%29+=+%28L%2B1%29%28L%2B1%29

L%5E2%2B%28L%5E2-2L%2B1%29+=+L%5E2%2B2L%2B1

L%5E2%2BL%5E2-2L%2B1+=+L%5E2%2B2L%2B1
L%5E2-4L+=+0
L(L – 4) = 0

L = 0, or L = 4.

Since the length CANNOT be 0, we reject L = 0, and therefore, L = 4.
Since L, or length = 4, then the width = L – 1 = 4 – 1 = 3.
B.
The diagonal of a rectangle that has sides of length 5’ and 12’ will be 13’, based on the 5-12-13 triangle.
OR
Using Pythagorean, we get:
a%5E2%2Bb%5E2+=+c%5E2
5%5E2%2B12%5E2+=+D%5E2
25%2B144+=+D%5E2
169+=+D%5E2
sqrt%28169%29+=+sqrt%28D%5E2%29
13 = D
Therefore, the diagonal of the rectangle is 13’.