# Algebra and Geometry Problems (Factoring/Rational expressions)

```ALGEBRAANDGEOMETRYPROBLEMS
1. Thefollowingcirclehasacircumferencethatisequaltotheperimeterofanisosceles
triangle.Findanexpressionforoneoftheothertwosidesofthetriangle.
x2-16
18x2+24x
2. Anisoscelestrianglehasabaseof 4 # + 8 − 8andtheinteriorheightofthetriangle
is 3( + 3).Findanalgebraicexpressionforeachoftheothertwosidestothe
triangle.
3. Aconeandsphereareequivalentinvolume.Theheightoftheconeisexpressedbythe
algebraicexpression
algebraicexpression
#* #+ , -..+/.0
+/#
1+ , /2+/3
+-1
.
b. Findanalgebraicexpressionforthesurfaceareaofthesphere.
4. Asphereandacylinderhavethesamesurfaceareas.Ifboththesphereandthecylinder
+ , -+-.#
#+ , -4+-*
findanalgebraicexpressionfortheheightofthecylinder.
5. Arightangletrianglehastwoshortersideswhicharerepresentedby(3x-5)unitsand
(4x+8)unitsrespectively.Thehypotenuseisrepresentedby(5x+5)units.Findthevalue
ofx.
6. Arhombusandarightangletrianglehaveequalperimeters.Thetwoshortersidesof
therightangletriangleare −16 + 8 and(2 + 1),respectively.
a. Findthemissingsideofthetriangle.
b. Findanexpressiontorepresentthelengthofonesideoftherhombus.
c. Whatvaluesofxproduceapossiblesolution?
7. Giventhatthefollowingtwofigureshaveequivalentvolumes,findthevalueofx
( + 4)
( # + 6 + 5)
−2
# − 2 − 24
−6
# + 7 + 12
+5
2 # − 6 − 8
−2
```