Advertisements
Advertisements
प्रश्न
The length of the sides of a triangle are in the ratio 3: 4: 5. Find the area of the triangle if its perimeter is 144 cm.
उत्तर
Let the sides of the triangle are
a = 3x
b = 4x
c = 5x
Given that the perimeter is 144 cm.
Hence
3x + 4x + 5x = 144
⇒ 12x = 144
⇒ x = `144/12`
⇒ x = 12
s = `(a + b + c)/(2)`
= `(12x)/(2)`
= 6x
= 6 × 12
= 72
The sides are a = 36 cm, b = 48 cm and c = 60 cm.
Area of the triangle is
A = `sqrt (s(s - a )( s - b ) (s - c ))`
= `sqrt (72(72 - 36 )( 72 - 48 ) (72 - 60))`
= `sqrt (72 xx 36 xx 24 xx 12)`
= `sqrt746496`
= 864 cm2
APPEARS IN
संबंधित प्रश्न
In triangle ABC; angle A = 90o, side AB = x cm, AC = (x + 5) cm and area = 150 cm2. Find the sides of the triangle.
The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m2 is ₹ 49,572; find its base and height.
Find the area of a triangle, whose sides are :
10 cm, 24 cm, and 26 cm
Find the area of a triangle, whose sides are :
18 mm, 24 mm and 30 mm
The sides of a triangle are 16 cm, 12 cm, and 20 cm. Find :
(i) area of the triangle ;
(ii) height of the triangle, corresponding to the largest side ;
(iii) height of the triangle, corresponding to the smallest side.
Find the area of a triangle whose sides are 27 cm, 45 cm and 36 cm.
The base of a triangle field and its height are in the ratio 2:5. If the cost of cultivating the field at Rs.42 per sq. m is Rs.7560, find its base and height.
The cost of fencing a triangular field at the rate of Rs.15 per m is Rs.900. If the lengths of the triangle are in the ratio 3:4:5, find the area of the triangle and the cost of cultivating it at Rs.48 per kg sq.m.
Find the perimeter of the triangle, whose sides are 13 cm, 5 cm and 14 cm
In the given figure, all triangles are equilateral and AB = 8 units. Other triangles have been formed by taking the mid points of the sides. What is the perimeter of the figure?
