Q9 of 50 Page 13

The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.

Sides of triangle are in ratio: 3 : 4 : 5



Since the perimeter of a triangle is given by:






Therefore sides of the triangle are:





When a, b and c are the sides of triangle and s is the semi-perimeter, then its area is given by:


A = where [Heron’s Formula]


= = 72


A =


A = = cm2


Area of triangle =


864 =


Altitude = 28.8 cm


More from this chapter

All 50 →
7

The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.

 8

A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes.

 10

The perimeter of an isosceles triangle is 42 cm and its base is (3/2) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.

 11

Find the area os the shaded region in Fig. 12.12.