   Chapter 4.CM, Problem 54CM

Chapter
Section
Textbook Problem

One leg of a right triangle is 7 inches less than the other leg. The hypotenuse is 1 inch longer than the longer of the two legs. Find the length of the three sides of the right triangle.

To determine

To Solve:

The sides of the right triangle.

Explanation

Procedure used:

“Model and solve system of linear equations”

(1) Identify the given problem.

(2) Recognize and algebraically name the unknowns.

(3) Translate the problem statement as a system of linear equations using the variables from Step 2.

(4) Solve the system as obtained in Step 3.

(5) State the answer statement.

Calculation:

Step 1:

The given problem is based on sides of the right triangle.

Step 2:

There are three unknowns in the problem. Let x be the one leg and x7 be the other leg. So, the hypotenuse is x+1.

Step 3:

The sum of square of smaller sides is equal to the square of larger side in right angle triangle.

x2+(x7)2=(x+1)2…(1)

Step 4:

From equation (1),

x2+(x7)2=(x+1)2x2+

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