Advertisements
Advertisements
Question
The sides of a triangle are in the ratio 5:12:13 and its perimeter is 150 m. Find the area of the triangle.
Solution
Let the sides of a triangle be `5xm,12xm and 13xm`
Since, perimeter is the sum of all the sides,
`5x+12x+13x=150`
⇒` 30x=150`
Or, `x=150/30=5`
The lengths of the sides are:
`a=5xx5=25m`
`b=12xx5=60m`
`c=13xx5=65 m`
Semi-perimeter (s) of the triangle = `"perimeter"/2=(25=60+65)/2=150/2=75m`
Area of triangle= `sqrt(s(s-a)(s-b)(s-c))`
=`sqrt(75(75-25)(75-60)(75-65))`
=`sqrt(75xx50xx15xx10)`
=`sqrt(562500)`
=`750m^2`
APPEARS IN
RELATED QUESTIONS
Find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles. [Use Π = 22/7]
In the given figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region. [Use Π = 22/7]
On a square handkerchief, nine circular designs each of radius 7 cm are made (see the given figure). Find the area of the remaining portion of the handkerchief.[Use Π = 22/7]
Calculate the area of the designed region in the given figure common between the two quadrants of circles of radius 8 cm each. [Use Π = 22/7]
The perimeter of a right triangle is 40 cm and its hypotenuse measure 17 cm. Find the area of the triangle.
Each side of an equilateral triangle is 10 cm. Find (i) the area of the triangle and (ii) the height of the triangle.
If the area of an equilateral triangle is `81sqrt3 cm^2` find its height.
A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away on time, it has to increase its speed by 250 km/hr from its usual speed. Find the usual speed of the plane.
Read the following passage:
|
For the inauguration of 'Earth day' week in a school, badges were given to volunteers. Organisers purchased these badges from an NGO, who made these badges in the form of a circle inscribed in a square of side 8 cm.
|
Based on the above information, answer the following questions:
- What is the area of square ABCD?
- What is the length of diagonal AC of square ABCD?
- Find the area of sector OPRQO.
OR
Find the area of remaining part of square ABCD when area of circle is excluded.
In the given figure, AB and CD are diameters of a circle with centre O perpendicular to each other. If OA = 7 cm, find the area of shaded region.
