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The altitude of a triangle is 6 cm greater than its base. If its area is 108 cm
2
. Find its base and height.
Hard
Solution
verified
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Let the base of the triangle be x.
It is given that the altitude of the triangle is 6 cm greater than its base, therefore, the altitude of the triangle is (x+6).
It is also given that the area of the triangle is 108 cm
2
.
We know that the area of the triangle is A=
2
1
×b×a, therefore,
108=
2
1
(x)(x+6)
⇒x
2
+6x=108×2
⇒x
2
+6x=216
⇒x
2
+6x−216=0
⇒x
2
+18x−12x−216=0
⇒x(x+18)−12(x+18)=0
⇒(x−12)=0,(x+18)=0
⇒x=12,x=−18
Since the length of the triangle cannot be negative thus, x=12.
Hence, the base of the triangle is 12 cm
