Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Find the area of an isosceles triangle with perimeter is 36 cm and the base is 16 cm.
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.
The area of an equilateral triangle is `144sqrt3` cm2; find its perimeter.
The altitude and the base of a triangular field are in the ratio 6: 5. If its cost is ₹ 49,57,200 at the rate of ₹ 36,720 per hectare and 1 hectare = 10,000 sq. m, find (in metre) dimensions of the field.
Find the area of a triangle whose sides are in the ratio 5:12:13 and whose perimeter is 36cm.
Find the area of a triangle with a base 12cm and a height equal to the width of a rectangle having area of 96cm2 and a length of 12cm.
The table given below contains some measures of the triangle. Find the unknown values.
| Side 1 | Side 2 | Side 3 | Perimeter |
| 6 cm | 5 cm | 2 cm | ? |
A piece of wire is 36 cm long. What will be the length of each side if we form an equilateral triangle
Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.
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?
