Question

The measurements of the sides of a triangle are 13cm,13cm, and 10cm.Find the area of this triangle . Find the length of altitude on the side of length 10 cm.​

Answer 1

Let

A= 13cm
B= 13cm
C= 10cm

Now, perimeter of the triangle= (13+13+10)cm

=> perimeter of the triangle= 36cm

Therefore, semi perimeter of the triangle= 36/2 cm

=> s= 18 cm

Now, by HERON'S FORMULA,

ar(triangle)= √[s(s-A)(s-B)(s-C)]

=>ar(triangle)= √[18(18-13)(18-13)(18-10)]

=>ar(triangle)= √[18×5×5×8 × cm⁴]

=>ar(triangle)= √3600cm⁴

=>ar(triangle)= 60cm²----(a)

Now, let the altitude on side C= 10cm be "X"

ar(triangle)= 1/2 × 10cm × X { taking the side with 10cm as base }

=> 60cm²= 5Xcm {from (a)}

=>X= (60cm²)/(5cm)

=>X= 12cm

THEREFORE X= 12cm (WHICH IS THE REQUIRED ALTITUDE)

AND THE AREA OF THE TRAINGLE IS *60CM²*!!!

Answer 2

Area of triangle= 60cm²

Altitude on the side of length 10cm= 12cm