SOLUTION: use let statemants. Show all step and all work. Jim has a rectangular table. The length of the table is 2 feet greater than the width of the table. A diagonal across the table i

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Question 966127: use let statemants. Show all step and all work.
Jim has a rectangular table. The length of the table is 2 feet greater than the width of the table. A diagonal across the table is 4 feet greater than the width of the table. Find the length of the diagonal across the table.
Answer by Theo(13342) (Show Source):
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let x equal the number of feet in the width.

you get width = x.

the length is 2 feet greater than the width.

you get length = x + 2

the diagonal across the table is 4 feet greater than the width of the table.

you get diagonal = x + 4

the length and the width and the diagonal form a right triangle where the length is one leg and the width is another leg and the diagonal is the hypotenuse.

use the pythagorean formula to find x.

based on the pythagorean formula, you get hypotenuse squared = length squared plus width squared.

this becomes:

x^2 + (x+2)^2 = (x+4)^2

simplify by performing the indicated operations to get:

x^2 + x^2 + 4x + 4 = x^2 + 8x + 16

combine like terms to get:

2x^2 + 4x + 4 = x^2 + 8x + 16

subtract all the terms on the right side of the equation from both sides of the eqution to get:

2x^2 + 4x + 4 - x^2 - 8x - 16 = 0

combine like terms to get:

x^2 - 4x - 12 = 0

factor that quadratic equation to get:

(x-6) * (x+2) = 0

solve for x to get x = 6 or x = -2

x can't be negative so x = 6.

when x = 6, you get:

x = 6 which is the length.
x + 2 = 8 which is the width.
x + 4 = 10 which is the diagonal.

the requriement was:

Find the length of the diagonal across the table.

the solution is:

the length of the diagonal across the table is 10 feet.