The base of a triangle is 4cm longer than altitude. If the area of the triangle is 48 square cm. Then find base and height
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Let base = b and altitude= h.
now, b= h+4
area of triangle = 1/2 × b×h
48 = 1/2 x (h+4) x h
96 = h^2+ 4h
0 = h^2 + 4h -96
0 = h^2+ 12h - 8h -96
0 = h(h+12) - 8(h+12)
0 = (h+12) (h-8)
so either h+12 = 0 or h-8 =0
so h= -12 cm or h= 8 cm.
as length cannot be negative
so h= 8 cm and b=h+4 = 12cm
now, b= h+4
area of triangle = 1/2 × b×h
48 = 1/2 x (h+4) x h
96 = h^2+ 4h
0 = h^2 + 4h -96
0 = h^2+ 12h - 8h -96
0 = h(h+12) - 8(h+12)
0 = (h+12) (h-8)
so either h+12 = 0 or h-8 =0
so h= -12 cm or h= 8 cm.
as length cannot be negative
so h= 8 cm and b=h+4 = 12cm
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