Question

The Base of triangle is 4cm longer then it's altitude. If the area of the triangle is 48 then find its based and altitude

Answer 1

Hey Mate!
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Here is your answer :

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Let the height of triangle be x

Base of triangle = x + 4

Area of triangle = 1/2 bh = 48

$\frac{1}{2} (x + 4)x = 48 \\ \\ {x}^{2} + 4x = 48 \times 2 \\ \\ {x}^{2} + 4x = 96 \\ \\ {x}^{2} + 4x - 96 = 0 \\ \\ {x}^{2} + 12x - 8x - 96 = 0 \\ \\ x(x + 12) - 8(x + 12) = 0 \\ \\ x + 12 = 0 \: \: x - 8 = 0 \\ \\ x = - 12 \: \: x = 8$
Height = 8cm as sides will not be negative.

Base = x + 4 = 8 + 4 = 12cm


HOPE THIS HELPS U...

Answer 2

let h = x and b= x+4
area= 1/2*h*b
48=1/2*h*b
96=x(x+4)
0=x^2+12x-8x-96
o=(x+12)or(x-8)
x=-12or x=8
so base=12 and altitude=8