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sveticcg [70]
3 years ago
15

△ABC is a right triangle with right angle C. Side AC¯¯¯¯¯¯¯¯ is 6 units longer than side BC¯¯¯¯¯¯¯¯. If the hypotenuse has lengt

h 217−−√ units, find the length of AC¯¯¯¯¯¯¯¯.
Mathematics
1 answer:
Vladimir [108]3 years ago
6 0

Given:

In △ABC is a right angle triangle.

AC is 6 units longer than side BC.

Hypotenuse=2\sqrt{17}

To find:

The length of AC.

Solution:

Let the length of BC be x.

So, Length of AC = x+6

According to the Pythagoras theorem, in a right angle triangle

Hypotenuse^2=Base^2+Perpendicualar^2

△ABC is a right angle triangle and AC is hypotenuse, so

(2\sqrt{17})^2=(x)^2+(x+6)^2

68=x^2+x^2+12x+36            [\because (a+b)^2=a^2+2ab+b^2]

Subtract 68 from both sides.

0=2x^2+12x+36-68

0=2x^2+12x-32

0=2(x^2+6x-16)

Divide both sides by 2.

x^2+6x-16=0

Splitting the middle term, we get

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

x(x+8)-2(x+8)=0

(x+8)(x-2)=0

x=-8,2

Side cannot be negative, so x=2 only.

Now,

AC=x+6

AC=2+6

AC=8

Therefore, the length of AC is 8 units.

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