Question

A triangle has base 2x and height x – 3. The area of the triangle is 10 square inches. Complete the work to find the dimensions of the triangle. x(x – 3) = 10 x2 – 3x = 10 x2 – 3x – 10 = 0 (x – 5)(x + 2) = 0 What are the base and height of the triangle? The base is 10 inches and the height is 2 inches. The base is 2 inches and the height is 10 inches. The base is 5 inches and the height is 2 inches. The base is 10 inches and the height is 1 inch.

Answer 1

C.)

Explanation:

Answer 2

base 5 inches and height 2 inches

Explanation:

Area of triangle =
`(base * height)/(2)`

Using this formula and the info on base=2x and height = x-3,

we obtain:

`Area = 10 in^2 = (2x (x-3))/(2) = x(x-3)=x^2-3x`

Solve the quadratic equation:
`x^2-3x-10=0\\(x-5)(x+2)=0`

Therefore there are two solutions to this equation:

One when x=5 and the other when x=-2

This last option has no physical meaning because the base (or for the matter any side of a triangle) cannot be a negative number.

Therefore x=5

That means that the base (which is 2 times x) must be 2 times 5 = 10 inches,

and the height (which is x-3) must be 5 minus 3 that gives 2 inches