The area of a triangle is 12 in.^2 . the base of the triangle measures 2 in. more than twice the height of the triangle. find the measures of the base and height.

  base = 8 in; height = 3 in

Step-by-step explanation:

Let h stand for the height of the triangle. Then 2h+2 will be the base length, and the area is ...

  A = 1/2bh

  12 = 1/2(2h+2)(h) = (h+1)(h)

We know that factors of 12 that differ by 1 are 4 and 3, so we conclude ...

  h = 3

  2h+2 = 8

Both dimensions are in inches.

Comment on the solution

If you work through the solution of the quadratic, you find solutions are ...

  h = -4, h = 3

That is, the pairs (-4, -3) and (3, 4) are both pairs of (h, h+1) that have a product of 12.

The negative solution is extraneous.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°