the perimeter of an isosceles triangle is 42cm and its base is 1whole 1/2 times each of the equal sides find the length of each sidr of the trianglr and find the area of the triangle and the height of the triangle take √7=2.64
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Let the equal sides be ‘a’ cm.
the base = 1.5 * base
base = 3/2 * a
Perimeter = 42 cm ( Given )
a + a + 3/2 * a = 42
7a / 2 = 42
a = 42 * 2 / 7
a = 12 cm
Base = 3/2 * a
Base = 3/2 * 12
Base = 18 cm
Using Heron’s formula,
Area = sqrt ( s * (s-a) * (s-b) * (s-c)),
where s = (a+b+c)/2 and a,b,c are the sides
s = (12 +12+18) /2
s = 21 cm
Area = sqrt (21 * (21-12) *(21–12) * (21–18))
Area = sqrt (21 * 9 * 9 * 3 )
Area = 27 √7 cm²
the base = 1.5 * base
base = 3/2 * a
Perimeter = 42 cm ( Given )
a + a + 3/2 * a = 42
7a / 2 = 42
a = 42 * 2 / 7
a = 12 cm
Base = 3/2 * a
Base = 3/2 * 12
Base = 18 cm
Using Heron’s formula,
Area = sqrt ( s * (s-a) * (s-b) * (s-c)),
where s = (a+b+c)/2 and a,b,c are the sides
s = (12 +12+18) /2
s = 21 cm
Area = sqrt (21 * (21-12) *(21–12) * (21–18))
Area = sqrt (21 * 9 * 9 * 3 )
Area = 27 √7 cm²
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