Advertisements
Advertisements
प्रश्न
The lengths of the sides of a triangle are in the ratio 4: 5 : 3 and its perimeter is 96 cm. Find its area.
Advertisements
उत्तर
Let the sides of the triangle ABC be 4x, 5x and 3x
Let AB = 4x, AC = 5x and BC = 3x
Perimeter = 4x + 5x + 3x = 96
=> 12x = 96
⇒ x = `96/12`
∴ x = 8
∴ Sides are
BC = 3(8) = 24 cm, AB = 4(8) = 32 cm,
AC = 5(8) = 40 cm
Since (AC)2 = (AB)2 + (BC)2 [∵ (5x)2 = (3x)2 + (4x)2]
∴ By Pythagorus Theorem, ∠B = 90°
∴ Area of ΔABC = `1/2 ("BC")("AB") = 1/2 (24)(32)`
= `12 xx 32 = 384 "cm"^2`
APPEARS IN
संबंधित प्रश्न
If the difference between the sides of a right-angled triangle is 3 cm and its area is 54 cm2; find its perimeter.
Find the area of a triangle, whose sides are :
18 mm, 24 mm and 30 mm
Two sides of a triangle are 6.4 m and 4.8 m. If the height of the triangle corresponding to 4.8 m side is 6 m;
find :
(i) area of the triangle ;
(ii) height of the triangle corresponding to 6.4 m sides.
Use the information given in the adjoining figure to find :
(i) the length of AC.
(ii) the area of an ∆ABC
(iii) the length of BD, correct to one decimal place.
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.
Find the perimeter and the area of a right angled triangle whose sides are 6 feet, 8 feet and 10 feet
A piece of wire is 36 cm long. What will be the length of each side if we form an equilateral triangle
In the following 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?
Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.
In the following figures, perimeter of ΔABC = perimeter of ΔPQR. Find the area of ΔABC.
