The perimeter of an isoceles triangle is 42cm. The base is 1 1/2 times the equal side .Fin the length of each side.
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The perimeter of an isoceles triangle is 42cm. The base is 1 1/2 times the equal side .Fin the length of each side.
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Answer:
let yhe equal side be x
base be11x/2
a/q
x+x+11x/2=42
2x/2+2x/2+11x/2=42
15x/2=42
5x/2=14
5x=28
x=28/5 =5.6cm
equal side =5.6cm
base=11/2×5.6= 30.8 cm
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Given :
To Find :
Solution :
Let the equal sides of the isosceles triangle be x.
[Two sides are of equal length in an isosceles triangle]
We have been given that the third (base) is 11/2 times the equal side (x).
•°• Third side → 11x/2
Perimeter : Sum of all sides.
Perimeter of the given isosceles triangle is 42 cm.
[tex]\longrightarrow[/tex][tex]\sf{\dfrac{11}{2}\:\times\:x\:+\:x\:+\:x=\:42}[/tex]
[tex]\longrightarrow[/tex] [tex]\sf{\dfrac{11x}{2}\:+\:2x=42}[/tex]
[tex]\longrightarrow[/tex] [tex]\sf{\dfrac{11x+4x}{2}\:=42}[/tex]
[tex]\longrightarrow[/tex] [tex]\sf{\dfrac{15x}{2}=42}[/tex]
[tex]\longrightarrow[/tex] [tex]\sf{15x=42\:\times\:2}[/tex]
[tex]\longrightarrow[/tex] [tex]\sf{15x=84}[/tex]
[tex]\longrightarrow[/tex] [tex]\sf{x=\dfrac{84}{15}}[/tex]
[tex]\longrightarrow[/tex] [tex]\sf{x=5.6}[/tex]
Length of equal sides of the isosceles triangle is 5.6 cm.
The base is 11/2 of the equal side, i. e 5.6 cm.
[tex]\longrightarrow[/tex] [tex]\sf{Third\:side\:=\:\dfrac{11\:\times\:x}{2}}[/tex]
[tex]\longrightarrow[/tex] [tex]\sf{Third\:side\:=\:\dfrac{61.6}{2}}[/tex]
[tex]\longrightarrow[/tex] [tex]\sf{Third\:side\:=\:30.6\:}[/tex]
Sides of the isosceles triangle :
[tex]\large{\boxed{\sf{\purple{First\:\:two\:equal\:side=\:x\:=\:5.6\:cm}}}}[/tex]
[tex]\large{\boxed{\sf{\purple{Third\:side\:=\:30.6\:cm}}}}[/tex]