Advertisements
Advertisements
प्रश्न
Find the area of a triangle whose sides are in the ratio 5:12:13 and whose perimeter is 36cm.
Advertisements
उत्तर
Perimeter P of the triangle = P = 36cm
Ratio of the sides = 5:12:13
Let the constant of proportionality be k
⇒ 5k + 12k + 13k = 36
⇒ 30k = 36
⇒ k = `(36)/(30)`
= 1.2
∴ the sides are: 5 x 1.2, 12 x 1.2 and 13 x 1.2
i.e. 6cm, 14.4cm and 15.6cm
We know that, Area of a Triangle whose sides are a, b, and c and semiperimeter is s is given by `sqrt("s"("s" - "a")("s" - "b")("s" - "c")); "s" = ("a" + "b" + "c")/(2)`
For a triangle whose sides are 6cm, 2.4cm and 15.6cm
i.e. a = 6 b = 14.4cm and c = 15.6, s = `(36)/(2)` = 18
Area
= `sqrt(18(18 - 6)(18 - 14.4)(18 - 15.6)`
= `sqrt(18(12)(3.6)(2.4)`
= `sqrt(1866.24)`
= 43.2cm2.
APPEARS IN
संबंधित प्रश्न
Find the area of a triangle whose sides are 18 cm, 24 cm, and 30 cm. Also, find the length of altitude corresponding to the largest side of the triangle.
The perimeter of a triangle is 450 m and its side are in the ratio 12: 5: 13. Find the area of the triangle.
A field is in the shape of a quadrilateral ABCD in which side AB = 18 m, side AD = 24 m, side BC = 40m, DC = 50 m and angle A = 90°. Find the area of the field.
The lengths of the sides of a triangle are in the ratio 4: 5 : 3 and its perimeter is 96 cm. Find its area.
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.
Find the area of a triangle whose base is 3.8 cm and height is 2.8 cm.
Find the perimeter of An equilateral triangle with side 6 cm
A piece of wire is 36 cm long. What will be the length of each side if we form an equilateral triangle
A piece of string is 30 cm long. What will be the length of each side if the string is used to form an equilateral triangle?
Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is its third side?
