Question

The height of the triangle is 4 less than it’s base. The area is 30 square inches. Find length of the baee to the nearest inch

Answer 1

10 inches

Explanation:

The area of a triangle is expressed as
`1/2bh` where;

g b is the lenghth of the base

h is the height

If the height of the triangle is 4 less than it’s base, then h = b-4

Substituting h = b-4 into the formula we have;

`A = (1)/(2)*b*(b-4)`

Given Area of the triangle A = 30in²

30 =
`\frac{{b^(2)-4b} }{2}`

Cross multiplying;

60 = b²-4b

b²-4b-60 = 0

b²-10b+6b-60 = 0

b(b-10)+6(b-10)=0

(b+6)(b-10) = 0

b+6 = 0 and b- 10 = 0

b = -6 and 10

Choosing the positive base;

b = 10 in

The length of the base to the nearest inch is 10 inches