(☝️☝️the question)
The perimeter of an isosceles triangle is 42cm and it's base is 5/2 times each of the equal sides find the length of each side of the triangle, area of the triangle and the height of the triangle.
(please it's urgent)
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Ans. Let the two equal sides be x
Base = (3x/2)
Perimeter of triangle= sum of all sides
42 cm = x+x+(3x/2)
42 cm = (2x+2x+3x)/2
42×2 = 7x
(42×2)/7 = x
12 cm = x
1st side = 2nd side = 12 cm
Base = 3rd side = 3/2×12 = 18 cm
Area of Isosceles triangle ABC =
By Heron's Formula,
a=b= 12cm ,c= 18 cm
Perimeter = 42 cm
Semiperimeter (s)= 42/2 cm = 21 cm
s-a = 21-12= 9 cm
s-b = 21-12= 9 cm
s-c = 21-18= 3 cm
Area of Isosceles ∆ =
√s(s-a)(s-b)(s-c) = √21×9×9×3
= 27√7 cm^2
Height of Isosceles ∆ =
1/2×base×height = Area of triangle
1/2 × 18 × height = 27√7 cm^2
Height of the ∆ = 27√7÷ 9
= 3√7 cm
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