side of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm find its area
Answers
Solution!!
The sides of the triangle are given in a ratio. The perimeter of the triangle is also given. We have to find the area of the triangle. To do so, we need to find all the three sides of the triangle.
Let the sides be 12x, 17x and 25x, respectively.
Perimeter of triangle = Sum of all sides
540 cm = 12x + 17x + 25x
540 cm = 54x
540 cm ÷ 54 = x
x = 10 cm
12x = 12 × 10 cm = 120 cm
12x = 12 × 10 cm = 120 cm17x = 17 × 10 cm = 170 cm
12x = 12 × 10 cm = 120 cm17x = 17 × 10 cm = 170 cm25x = 25 × 10 cm = 250 cm
Verification of the sides:-
540 cm = 12x + 17x + 25x
Taking RHS
= 120 cm + 170 cm + 250 cm
= 540 cm
LHS = RHS
Hence, verified
Now that we have the sides of the triangle, let's find out the area. I'll use the Heron's formula.
Semi-perimeter (s) = (a + b + c)/2
Here a, b and c are the sides.
s = 540 cm/2
s = 270 cm
Area = √[s(s-a)(s-b)(s-c)]
Area = √[270(270-120)(270-170)(270-250)]
Area = √[270(150)(100)(20)]
Area = 9000 cm²