Question

The longer leg of the right triangle is 8 more than the shorter leg. The hypotonuse is 8 more than the longer leg. FInd all 3 sides

Answer 1

Answer:

4$\sqrt{13}$

4$\sqrt{13}$ + 8

4$\sqrt{13}$ + 16

Step-by-step explanation:

as per the given information:

shorter leg = x

longer leg = x + 8

hypotonuse = x + 8 + 8

remember the Pythagorean theorem, which states

x^2 + y^2 = n^2

where x and y are the legs and n is the hypotenuse

so now one can set up an equation:

x^2 + ( x + 8 )^2 = ( x + 16 ) ^2

simplify and solve using inverse operations:

first preform the square

x^2 + x^2 + 16x + 64 = x^2 + 32x + 256

then preform inverse opertations and simplify

2x^2 + 16x + 64 = x^2 + 32x + 256

-x^2                       -x^2

x^2 + 16x + 64 = 32x + 256

       -16x            -16x

x^2 + 64 = 16x + 256

       - 64             -64

x^2 = 16x + 192

-16x     -16x

x^2 - 16 = 192

x^2 -4^2 = 192

remember the differnt ways of writing a special square

(x - 4) (x + 4) = 192

x = 4$\sqrt{13}$

now add 8 to find the longer leg

4$\sqrt{13}$ + 8

an add another 8 to find the hypotenuse

4$\sqrt{13}$ + 8 + 8

4$\sqrt{13}$ + 16