Question

The area of a right triangle is 49 square inches. The base is

Answer 1

Answer:

height: 7 in

base: 14 in

Step-by-step explanation:

Let the height of the triangle equal x. This means that the base can be represented by the expression 2x. Now we plug these values into the area formula for a triangle:

A = bh / 2

49 = x * 2x / 2

And simplify

49 = x^2

We can find the square root of both sides to get x = 7, so the height is 7 inches. Since the base is twice the height, it is 14 inches.

Answer 2

Answer:

$h=7,\\b=14$

Step-by-step explanation:

Since the base is twice as long as the height, set up the following proportion:

$b=2h$.

The area of the a right triangle is equal to $A=\frac{1}{2}bh$, where $b$ is a base of the triangle and $h$ is the respective height.

To solve for height, set up the equation (substituing $b=2h$:

$\frac{1}{2}\cdot2h\cdot h=49,\\2h^2=98,\\h^2=49,\\h=\boxed{7}$

To solve for base, substitute $h=7$ in the proportion $b=2h$:

$b=2(7),\\b=\boxed{14}$