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

4
`√(13)`

4
`√(13)` + 8

4
`√(13)` + 16

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
`√(13)`

now add 8 to find the longer leg

4
`√(13)` + 8

an add another 8 to find the hypotenuse

4
`√(13)` + 8 + 8

4
`√(13)` + 16