What is the width of a triangle where the width is 14 less than the length and the area is 176?

Answer 1

The width of this triangle is 13.025 (to 3 decimal places only).

We know that the area of a triangle = length * width (usually called height but width will do) / 2.

If we substitute the variable "x" for the length, then the width will equal "x - 14" and we can write the following equation:

(x * (x - 14)) / 2 = 176

We can multiply out the first bracket to get:

(x2 - 14x) / 2 = 176

Now we can multiply both sides of the equation by 2 to get:

x2 - 14x = 352

We can now subtract 352 from both sides of the equation in order to rewrite this in the form of a quadratic equation:

x2 - 14x - 352 = 0

We can now use the quadratic formula to solve for the roots:

Where ax2 + bx + c = 0 then:

x = (-b + or - (b2 - 4ac)1/2) / 2a

x = (--14 + or - (-142 - (4 * 1 * -352))1/2) / 2 * 1

x = (14 + or - (196 - - 1408)1/2) / 2

x = (14 + or - 16041/2) / 2

You can now calculate this to the desired level of accuracy.

I will answer to 3 decimal places:

x = 27.025 & -13.025 (both to 3 decimal places only)

We can ignore the negative root as this can't be a real solution. Therefore the length is equal to 27.025. Thus the width = 27.025 - 14 = 13.025.

Note: this answer will not provide an area of exactly 176 because the dimensions are provided accurate only to 3 decimal places. If you require a more accurate answer then you must perform the above calculation to a greater level of accuracy (i.e. to more than 3 decimal places).