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The area of a right triangle is 49 square inches. The base is
twice as long as the height. The formula for the area of a
triangle is A = 1/2 bh, where b is the base and h is the height.
How long is the base and how tall is the height?

Respuesta :

aklee18oo

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.

Corsaquix

Answer:

[tex]h=7,\\b=14[/tex]

Step-by-step explanation:

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

[tex]b=2h[/tex].

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

To solve for height, set up the equation (substituing [tex]b=2h[/tex]:

[tex]\frac{1}{2}\cdot2h\cdot h=49,\\2h^2=98,\\h^2=49,\\h=\boxed{7}[/tex]

To solve for base, substitute [tex]h=7[/tex] in the proportion [tex]b=2h[/tex]:

[tex]b=2(7),\\b=\boxed{14}[/tex]

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