Question

The area of right triangle is 150cm square. If it's altitude exceed the Base by 5cm . Calculate perimeter of triangle

Answer 1

Given altitude of triangle exceeds base by 5 cm
Let the base be x cm
Therefore, altitude= (x + 5) cm
Area of triangle = (1/2) x base x altitude
150 = (1/2) × (x + 5) × (x)

multiplying x intobracket,

300 = x² + 5x
x² + 5x - 300 = 0
discriminant value
x= -b +/- root (b^2-4ac)
-------------------------
2a

-5 +root (25-4*1*(-300))
----------------------------
2a

-5 + root (1225)
----------------------
2

-5 +35 -5-35
-------- and -------
2 2

15 and -20


so only positive because length not be negative



Hence x = 15 cm
That is base = 15 cm
altitude = 15+5=20 cm





now area = 1/2 bh = 1/2 15*20 =150
correct