Question
Asked Nov 1, 2019

The first leg of a right triangle is 2 cm longer than its second leg. If the hypotenuse has a length of 4 cm, find the exact lengths of the two legs.

 

check_circleExpert Solution
Step 1

Let the length of the second leg be x.

Then the length of the first leg is x+2.

From the given, the length of the hypotenuse is 4 cm.

By Pythagorean Theorem, for a right triangle,

C
b
a2+b2-c2
where c is hypotenuse
Then for the given triangle,
(x+2)+(x)2 4)2
x2+4x+4+x2=16
2x2+4x-12=0
help_outline

Image Transcriptionclose

C b a2+b2-c2 where c is hypotenuse Then for the given triangle, (x+2)+(x)2 4)2 x2+4x+4+x2=16 2x2+4x-12=0

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Step 2

Solving the quadratic e...

-4t424.2-12
2.2
-4t 112
2.2
-4+ 47
Since length cannot be negative, so r= -1+7
Then the length of the first leg is, x+2 (-1+7)
+2=17
Thus, the exact lengths of the two legs are -1+7,1+/7.
help_outline

Image Transcriptionclose

-4t424.2-12 2.2 -4t 112 2.2 -4+ 47 Since length cannot be negative, so r= -1+7 Then the length of the first leg is, x+2 (-1+7) +2=17 Thus, the exact lengths of the two legs are -1+7,1+/7.

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Algebra