Question

The height of a triangle is 4 m less than its base. The area of the triangle is 48 m².

What is the length of the base?

Answer 1

The area of a triangle is always:

A=bh/2, we are told that A=48 and h=b-4 so:

48=(b/2)(b-4)

48=(b^2-4b)/2

b^2-4b=96

b^2-4b-96=0

b^2-12b+8b-96=0

b(b-12)+8(b-12)=0

(b+8)(b-12)=0, and since b>0

b=12m

Answer 2

let the base be x metres.

1/2 × (x) × (x - 4) = 48
(x) × (x - 4) = 48 ÷ 1/2
(x) × (x - 4) = 96
x^2 - 4x = 96
x^2 - 4x - 96 = 0
(x - 12) (x + 8) = 0
x = 12 or -8 (rejected, since length of base must be positive)

therefore the length of the base (x) = 12m

-

hope this helps :)))