A triangle is 6 cm wider than it is tall. The area is 36 cm^(2). Find the height and the base?

Answer 1

To find the height and base of the triangle, we can set up the following equations based on the given information:

Let the height of the triangle be x cm. Then, the base of the triangle would be (x + 6) cm.

The formula for the area of a triangle is A = 0.5 * base * height. Given that the area is 36 cm^2, we can substitute the values into the formula:

36 = 0.5 * (x + 6) * x 36 = 0.5x^2 + 3x 0 = 0.5x^2 + 3x - 36

Now, we can solve for x by using the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / 2a

In this case, a = 0.5, b = 3, and c = -36. Plugging in these values: x = [-3 ± sqrt(3^2 - 4 * 0.5 * -36)] / 2 * 0.5 x = [-3 ± sqrt(9 + 72)] / 1 x = [-3 ± sqrt(81)] / 1 x = [-3 ± 9] / 1

Now, we have two possible solutions for x:

x = (-3 + 9) / 1 = 6

x = (-3 - 9) / 1 = -12 (not a valid height for a triangle)

Therefore, the height of the triangle is 6 cm. The base of the triangle is x + 6 = 6 + 6 = 12 cm.

So, the height is 6 cm and the base is 12 cm.