Advertisements
Advertisements
Question
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Advertisements
Solution
Let the common ratio between the sides of the given triangle be x.
Therefore, the side of the triangle will be 12x, 17x, and 25x.
Perimeter of this triangle = 540 cm
12x + 17x + 25x = 540 cm
54x = 540 cm
x = 10 cm
Sides of the triangle will be 120 cm, 170 cm, and 250 cm.
s = `"perimeter of triangle"/2`
= `540/2`
= 270 cm
By Heron's formula,
Area of triangle = `sqrt(s(s-a)(s-b)(s-c))`
= `[sqrt(270(270-120)(270-170)(270-250))]cm^2`
= `[sqrt(270xx150xx100xx20)]cm^2`
= `sqrt(10^2 xx 10^2 xx 3^2 xx 3^2 xx 5^2 xx 2^2) cm^2`
= (10 × 10 × 3 × 3 × 5 × 2) cm2
= 9,000 cm2
Therefore, the area of this triangle is 9,000 cm2.
APPEARS IN
RELATED QUESTIONS
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
Find the area of an isosceles triangle having the base x cm and one side y cm.
Find the areas of the given plot. (All measures are in metres.)
Determine whether the sets of points are collinear?
`(-1/2, 3), (-5, 6) and (-8, 8)`
Find the area of triangle AGF
Find the area of the unshaded region
The area of the isosceles triangle is `5/4 sqrt(11)` cm2, if the perimeter is 11 cm and the base is 5 cm.
The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.
A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1 m2 of the field, find the total cost of ploughing the field.
