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