The perimeter of an isosceles triangle is 42cm and its base is 3/2 times each of the equal sides. Find the length of each side of the triangle and the height of the triangle.
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Step-by-step explanation:
two equal sides AB and AC be x & x
Base BC=
2
3
x
Perimeter=42
x+x+
2
3x
=42
2
3
x+2x=42
2
7x
=42
x=6×2=12
AB=AC=12
BC=
2
3
×12=18
In △ADC
AC
2
=AD
2
+DC
2
12
2
=AD
2
+9
2
144−81=AD
2
AD
2
=63
AD=
63
=3
7
Area of △ABC=
2
1
×AD×BC
=
2
1
×3
7
×18
=27
7
Height of triangle=AD=3
7
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