Question

the perimeter of an isosceles triangle is 42 cm and its base is one one by two times each of the equal sides find number 3/2the length of each side of the triangle number to the area of the triangle and number three the height of the triangle

Answer 1

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