Math question.. thank you.

Question

Bill uses mirrors to augment the “laser experience” at a laser show. At one show he places three mirrors, A ,B, C,  in a right triangular form. If the distance between A  and B is 8 m more than the distance between A and C, and the distance between B and C is 8 m less than the distance between A and C , what is the distance between mirror A and mirror C ? 

Answer 1

Since we are talking for a right triangle and AB is the longer side , we conclude that AB is the hypotenuse

of the triangle.

So

AC = x

BC = x- 8

AB = x + 8

Then applying the Pythagorean Theorem we have AB² = AC² + BC²

or equivalently ( x + 8 )² = x² + ( x - 8 )²

x² + 16 x + 64 = x² + x² - 16x + 64

32 x = x²

x (32 - x ) = 0

x= 32

Hence AC = 32

BC = 24

AB = 40

Answer 2

Hello Britney.

according to the given info; the sides are x, x -8, x +8 units

since it is right triangle, we can use the pythagorean theorem;

x^2 +(x - 8)^2. =(x +8)^2

when you solve it, the sides will be 24-32-40

distance between A and C should be x = 32 (it is the middle #)

hope that helps