The base of a triangle is 4cm greater than its altitude . If its area 48cm^2 find its base and altitude
Answers
ATQ, the base of the triangle is 4cm greater than it's altitude.
let the altitude be x.
therefore it's base = 4 + x
given the area of the triangle = 48cm²
➡ 1/2 × b × h = 48cm²
➡ 1/2 × (x + 4)(x) = 48cm²
➡ x(x + 4) = 48 × 2
➡ x² + 4x = 96
➡ x² + 4x - 96 = 0
➡ x² + (12x - 8x) - 96 = 0
➡ x² + 12x - 8x - 96 = 0
➡ x(x + 12) - 8(x + 12) = 0
➡ (x + 12) (x - 8) = 0
therefore x = -12 or x = 8
since altitude can't be in negative.
hence, the Altitude of the triangle = x = 8cm
and base of the triangle = 4 + x = 4 + 8 = 12cm
Answer:
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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