Question

The difference between the length of the hypotenuse and the length of the next longest side of a right triangle is 3 cm. The difference between the lengths of the two perpendicular sides is 3 cm. Find the three side lengths.

Answer 1

I don't get it..

Answer 2

call the hypotenuse length x:use the Pythagorean theorem:\[x^2=(x-3)^2+(x-6)^2\]and solve for x.

Answer 3

why is it x-3, and x-6?

Answer 4

as The difference between the lengths of the two perpendicular sides is 3 cm

Answer 5

So once I get: \[(x ^{2}-6x+9)(x ^{2}-12x+36)\]

Answer 6

what do I do after?

Answer 7

utzz...rong u r missin +sign in between

Answer 8

\[(x ^{2}-6x+9)+(x ^{2}-12x+36)=x ^{3}\]

Answer 9

ohh, yup I put that now. And so I add to: 2x^2 - 18x + 45?

Answer 10

imean....x^2

Answer 11

equate to x^2

Answer 12

huh?

Answer 13

so the equation becomes....... 2x^2 - 18x + 45=x^2

Answer 14

hence
2x^2 - 18x + 45-x^2=0

Answer 15

x^2 - 18x + 45?

Answer 16

x^2 - 18x + 45=0

Answer 17

=> (x-3)(x-15)=0

Answer 18

hence x=3 or x=15

Answer 19

got it?/

Answer 20

...and since x=3 will not produce a triangle we have x=15

Answer 21

yeah right...

Answer 22

ohh..