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8. The hypotenuse of a right triangle is 2 ft. less than three times the shorter leg. The longer leg is 3 ft. less than three times the shorter leg. Find the length of the shorter leg.

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The hypotenuse of a right triangle is 2 ft. less than three times the shorter leg. The longer leg is 3 ft. less than three times the shorter leg. Find the length of the shorter leg. ​

Let

c -----> the hypotenuse

a ----> the shorter leg

b ----> the longer leg

we have that

c=3a-2 -----> equation 1

b=3a-3 -----> quation 2

Applying the Pythagaroean Theorem

c^2=a^2+b^2

substitute

the values

(3a-2)^2=a^2+(3a-3)^2

solve for a

9a^2-12a+4=a^2+9a^2-18a+9

simplify

-12a+4=a^2-18a+9

a^2-18a+12a+9-4=0

a^2-6a+5=0

Solve teh quadratic equation

Solve by graphing

the solution is a=1 and a=5

see the attached figure

please wait a minute

Verify each solution of a

For a=1

c=3a-2 ------> c=3(1)-2=1

Is not a solution because c is the greater side

For a=5

c=3(5)-2=13

b=3(5)-3=12

therefore

the answer is

the shorter leg is 5 units

8. The hypotenuse of a right triangle is 2 ft. less than three times the shorter leg-example-1
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