Question

A city lot has the shape of a right triangle whose hypotenuse is 3 ft longer than one of the other sides. The perimeter of the lot is 396 ft. How long is each side of the lot?

Answer 1

have you covered quadratic equations yet? like, factoring quadratics by using FOIL

Answer 2

Yes

Answer 3

I made a graphic. That should help.

Answer 4

What do I do with this?

Answer 5

y^2 = (x+3)^2 -x^2
That should be
y^2 = (x+3)^2 -x^2 NOT + x^2
I'd say multiply it out

Answer 6

y^2 = (x+3)^2 -x^2
y^2 = x^2 + 6x + 9 -x^2
y^2 = 6x +9
y = sq root (6x + 9)

Answer 7

Okay now I have \[y^2=6x+9\]

Answer 8

Okay \[y=\sqrt{6x+9}\]

Answer 9

perimeter = 396 So,
396 = (x+3) + x + sq root (6x +9)

Answer 10

Square both sides
396^2 = x^2 + 6x + 9 + x^2 + 6x +9

Answer 11

156,816 = 2x^2 +12x +18

2x^2 +12x -156,798 =0

Can you solve that quadratic equation?

Answer 12

yeah

Answer 13

I'm thinking I didn't square that correctly.
396 = (x+3) + x + sq root (6x +9)

396^2 = (2x + 3 +sq root (6x+9))^2

Answer 14

(2x + 3 +sq root (6x+9))^2 =

(2x + 3 + sq root(6x +9) * (2x + 3 + sq root(6x +9)

Answer 15

Even if that is squared properly, there will still be a square root radical left in there.

Answer 16

The side lengths are not necessarily integers, so if one or more length comes out to contain a radical, don't worry about it.

Answer 17

Summing up the 3 side lengths: x + y + (x+3).
Simplify this expression, and then set it = to 396. Solve the resulting equation for y.
Then, substitute your expression for y into your diagram: Replace y with it. Solve the resulting equation for x. Finally, find y.