The perimeter of an isosceles triangle is 42 cm and its base is 1.5 times each of its equal sides find a) the length of each side of the triangle b) area of the triangle c)height of the triangle chapter: herons formula class 9
Answers
Let ‘x’ be the measure of each equal sides
∴ Base = 3/2x
∴ x + x + 3/2x = 42 b[ P=a + b + c = 42 cm]
7/2x = 42
x = 12 cm
∴ Sides are, a = x = 12 cm
b = x = 12 cm
c = x = 3/2(12) cm = 18 cm
s = 42/2 = 21 cm
By heron’s formula
Area of triangle = √s(s-a)(s-b)(s-c)
= √21(21-12)(21-12)(21-18)
= √21(9)(9)(3)
= 9√21(3)
= 9√7×3×3
= 9×3√7
= 27√7 cm²
area of triangle = 1/2×b×h
27√7 = 1/2×18×h
27√7 = 9×h
(27√7)/9 = h
3√7 cm = h
Therefore, the length of each side of the triangle are 12cm,12cm and 18cm
Area of the triangle is 27√7 cm²
Height of the triangle is 3√7 cm