Question

Find the area of the triangle whose perimeter is 22cm. One side measures 9cm and the difference of the other two sides is 3cm.

Answer 1

Let us assume the sides of triangle to be x , y, z 

Let the side x be = 9cm

Perimeter = 2s = 22cm

s = 11cm

Also perimeter is the sum of all sides

Hence x + y+ z = 22

9+ y + z = 22

y+z = 13—-(i)

Given that difference between two sides is 3 cm

Hence y – z = 3cm—–(ii)

 

On adding equations (i) and (ii) we get

 

y+z = 13

y – z = 3cm

2y = 16

y = 8

Hence on back substitution we get

z = 5

From the herons formula to determine the area of triangle we get

Area=√s(s−a)(s−b)(s−c)

Where “s” is semi-perimeter = (a+b+c) / 2

And a, b, c are the three sides of the triangle.

√11(11−9)(11−8)(11−5)

=6√11 cm²

 

 

Area of triangle is 6√11 cm².