Advertisements
Advertisements
प्रश्न
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Advertisements
उत्तर
Let the common ratio between the sides of the given triangle be x.
Therefore, the side of the triangle will be 12x, 17x, and 25x.
Perimeter of this triangle = 540 cm
12x + 17x + 25x = 540 cm
54x = 540 cm
x = 10 cm
Sides of the triangle will be 120 cm, 170 cm, and 250 cm.
s = `"perimeter of triangle"/2`
= `540/2`
= 270 cm
By Heron's formula,
Area of triangle = `sqrt(s(s-a)(s-b)(s-c))`
= `[sqrt(270(270-120)(270-170)(270-250))]cm^2`
= `[sqrt(270xx150xx100xx20)]cm^2`
= `sqrt(10^2 xx 10^2 xx 3^2 xx 3^2 xx 5^2 xx 2^2) cm^2`
= (10 × 10 × 3 × 3 × 5 × 2) cm2
= 9,000 cm2
Therefore, the area of this triangle is 9,000 cm2.
APPEARS IN
संबंधित प्रश्न
The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.
The perimeter of an isosceles triangle is 42 cm and its baše is (32) 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.
The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.
Find the area of the triangle formed by the points
(–10, –4), (–8, –1) and (–3, –5)
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is
Find the area of a triangle formed by the lines 3x + y – 2 = 0, 5x + 2y – 3 = 0 and 2x – y – 3 = 0
The perimeter of an equilateral triangle is 30 cm. The area is
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
In the following figure, ∆ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of ∆ABC is constructed. Find the height DF of the parallelogram.
