Solution : Let, the lengths of the sides of the triangle are a 7 cm., b 8 cm. and
c 9 cm.
? Semi perimeter
2
7 8 9
2
a b c
s cm. = 12 cm.? Its area = s(sa)(sb)(sc)
= 12 ( 12 7 )( 12 8 )( 12 9 ) sq. cm.
= 12 u 5 u 6 u 7 sq. cm. = 50 2 sq. cm. (approx)
? The area of the triangle is 50 2 sq. cm. (approx)
Example 4. The area of an equilateral triangle increases by 3 3 sq. metre when the
length of each side increases by 1 metre. Find the length of the side of the triangle.
Solution : Let, the length of each side of the equilateral triangle is a metre.
? Its area =^2
4
3
asq. m.The area of the triangle when the length of each side increases by 1m. = ( 1 )^2
4
3
asq. metre.
According to the question, 33
4
3
( 1 )
4(^322)
a a
or,(a 1 )^2 a^2 12 ; [dividee by
4
3
]
or, a^2 2 a 1 a^2 12 or, 2 a 11 or, a 5 5
The required length is 5 5 metre.
Example 5. The length of the base of an isosceles triangle is 60 cm. If its area is
1200 sq. metre, find the length of equal sides.
Solution : Let the base of the isosceles triangle be b 60 cm. and the length of
equal sides be a.
? Area of the triangle = 42 2
4
a b
b
According to the question, 4 1200
4
b a (^2) b (^2)
or, 4 ( 60 ) 1200
4
(^6022)
a
or, 154 a^2 3600 1200
or, 4 a^2 3600 80