Please Help! Algebra 2 Quadratic Word Problems?

Question

The hyptenuse of a right triangle is 3 cm longer than the larger leg of the triangle. The larger leg is 9 cm less than three times the length of the smaller leg. What is the area of the right triangle?

Equation:
Area of the Triangle:






The volume of Cleopatra's jewlery box is 648 cubic centimeters. If the bos is 3 cm high and the perimeter of its rectangle base is 60 centimeters, find all dimensions of the jewelery bos.

Equation:
Dimensions of the jewlery box:



Thank you so much for helping! I definitely appreciate it.

Answer 1

a= short side
b=long side=3a-9
c=hyp=3a-9+3=3a-6
a^2+b^2=c^2
subbing
a^2+(3a-9)^2=(3a-6)^2
multiply
a^2+9a^2-54a+81=9a^2-36a+36
subtracting
a^2-18a+45=0
factoring
(a-15)(a-3)=0
so a=15 or a=3
ifa=3 b=0 so forget 3
a=15 b=36 c=39
area=(ab)/2=(15*36)/2=270cm^2
---------------------------------------------
height=3 so base area =648/3=216
side=x and 1/2 the perimeter=30
x(30-x)=216
30x-x^2=216
0=x^2-30x+216
(x-12)(x-18)=0
x=12 or x=18
if we use 12 the other is 30-12=18
so the dim are 12x18x3cm

Answer 2

the triangle
rememeber that for a right triangle c^2=a^2+b^2 , where c is the hypotenuse and a and b are the other two side (it don't matter which is a or b)
the area of the triangle is axbx1/2, in this case do NOT use c
the box-- you are solving for length and a width, you were given the volume and the depth. The area of the rectangle is 648/3
216 is the area of length x width


ok
try this for the triangle
let a = x = the shortest side
let b= 3x-9
let c (hypo)= b+3 which = (3x-9)+3
then go c^2=a^2+b^2
WATCH OUT, exponents are NOT communitive!!!
remember Order of Operations!!!!
I got to 8X^2+18X-45 = 0


60 is the perimeter, 2xlength+2xwidth

30 = l + w
216 = (30-w) * w
or
w^2-30w+216=0

subtitutions will get you the rest of the way
mail me the answer if you want me to dblchck


I rushed the triangle!! go with Dino's answer!!
The box is correct! 12&18
nice job Dino!!