SOLUTION: The hypotenuse of a right triangle is 2 cm less than twice the shorter side. The longer side is 2 cm longer than the shorter side. How long is the hypotenuse?

Question 597607: The hypotenuse of a right triangle is 2 cm less than twice the shorter side. The longer side is 2 cm longer than the shorter side. How long is the hypotenuse?
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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Since this is a right triangle, we will use the Pythagorean Equation to find the lengths of the hypotenuse.
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[I] Define the variables
Call a the length of the short leg.
Call b the length of the long leg.
Call c the hypotenuse.
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[II] Create equation based on the given relationships
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By the Pythagorean Theorem, we have

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In algebra, "the hypotenuse is 2 cm less than twice the shorter side" can be written as

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Likewise, we can write "the longer side is 2 cm longer that the shorter side" as

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[III] Solve the system of equations
Substitute a+2 for b and 2*a-2 for c in the Pythagorean Equation.

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Use the distributive property to clear the parentheses.

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Simplify and solve for a.

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Factor the quadratic polynomial on the left side of the equation.

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By the Zero Product Property, is -2 times (a-6) equals zero, then (a-6) must equal zero.

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The equation a=6 means that the shorter leg of the triangle is 6 cm.
The longer leg is a+2 = 6+2 = 8 cm.
The hypotenuse is 2*a-2 = 2(6)-2 = 10 cm.
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[IV] Check your work
Do these values satisfy a right triangle?

Correct!
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THe hypotenuse is 10 cm.
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I hope this helps!
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Ms.Figgy
math.in.the.vortex@gmail.com
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