Advertisements
Advertisements
Question
Find the area of a triangle whose sides are in the ratio 5:12:13 and whose perimeter is 36cm.
Advertisements
Solution
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
RELATED QUESTIONS
Calculate the area and the height of an equilateral triangle whose perimeter is 60 cm.
The area of an equilateral triangle is 36`sqrt3` sq. cm. Find its perimeter.
Find the area and the perimeter of quadrilateral ABCD, given below; if AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90°.
The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.
Find the area of a triangle, whose sides are :
18 mm, 24 mm and 30 mm
Two sides of a triangle are 6 cm and 8 cm. If the height of the triangle corresponding to 6 cm side is 4 cm; find :
(i) area of the triangle
(ii) height of the triangle corresponding to 8 cm side.
The lengths of the sides of a triangle are in the ratio 4: 5 : 3 and its perimeter is 96 cm. Find its area.
Find the area of a triangle whose base is 3.8 cm and height is 2.8 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.
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?
