AREA OF TRIANGLE

Find the base of the following triangle if its area is 10.5 cm

Solution

Area =  1 x base x  height

               2

10.5 =  1  x   (a-4) x  a

              2

2 x 10.5 =  1 x (a-4) x  a x 2¹

                    2 

21 =  1  x  (a-4)a

a (a-4)   = 21

a² – 4a = 21       

           

a² – 4a - 21= 0 [solving it by factorization]

a² + 3a - 7a - 21= 0

(a² + 3a) – (7a – 21)= 0

a(a + 3) –7 (a + 3)= 0

       

(a – 7)(a + 3) = 0

a – 7=0  OR  a + 3 = 0

a =7  OR  a = -3

Since there is no negative length, we take a=7.

Base = a – 4

           = 7 – 4

           = 3

Hence the base is 3cm.