Question

The width of a triangle is six more than twice the height. The area of the triangle is 88in2. Find the height and base of the triangle.

Answer 1

For this case we have that by definition, the area of a triangle is given by:

$A = \frac {b * h} {2}$

Where:

b: It is the base of the triangle

h: It is the height of the triangle

According to the statement data we have:

$b = 6 + 2h$

Substituting we have:

$88 = \frac {(6 + 2h) * h} {2}\\176 = 6h + 2h ^ 2\\2h ^ 2 + 6h-176 = 0$

We divide between 2 on both sides:

$h ^ 2 + 3h-88 = 0$

We factor by looking for two numbers that, when multiplied, are obtained -88 and when added together, +3 is obtained.

These numbers are +11 and -8.

$(h + 11) (h-8) = 0$

We have two roots:

$h = -11\\h = 8$

We choose the positive value.

Thus, the base of the triangle is:$b = 6 + 2 (8) = 22$

Answer:

The base of the triangle is 22 units.

Answer 2

Answer: The height and base of the triangle is 8 in and 22 in respectively.

Step-by-step explanation:

Let the height of the triangle be 'x' units

We are given a statement:

Base is six times more than twice the height

'More' in the above statement means addition operation.

'Twice' in the above statement means multiplication operation having factor '2'.

So, the equation becomes:

Base, b = 6 + 2x        .......(1)

We know that:

Area of a triangle = $\frac{1}{2}\times b\times h$         .......(2)

We are given:

Area of the triangle = $88in^2$

Putting values and the expression of breadth from equation 1 in equation 2, we get:

$88=\frac{1}{2}\times (6+2x)\times x\\\\x^2+3x+88=0\\\\x=8,-11$

Neglecting the value x = -11 because height of the triangle cannot be negative.

So, height of the triangle = 8 inches

Base of the triangle = $(6+2x)=(6+(2\times 8))=22in$

Hence, the height and base of the triangle is 8 in and 22 in respectively.