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 = ~~2~~

__1__x (a-4) x a x^{1}
21
= 1
x (a-4)a

a (a-4)
= 21

a

^{2}– 4a = 21
a

^{2}– 4a - 21= 0 [solving it by factorization]
a

^{2}+ 3a - 7a - 21= 0
(a

^{2}+ 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.__

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