the area of a triangle is 338 square yards. the height of the triangle is four times its base find the height and base of the triangle

let base be x yds
then height is 4x yds

area of triangle = base x height/2
= x(4x)/2 = 2x^2

but 2x^2 = 338
x^2 = 169
x = √169 = 13

etc.

To find the height and base of the triangle, we'll use the formula for the area of a triangle:

Area = (base * height) / 2

Given that the area is 338 square yards, we can substitute this value into the formula:

338 = (base * height) / 2

We also know that the height is four times the base, so we can express the height in terms of the base as:

height = 4 * base

Substituting this expression for height into the equation, we get:

338 = (base * (4 * base)) / 2

Now we can solve for the base:

338 = (4 * base^2) / 2
338 = 2 * base^2
base^2 = 338 / 2
base^2 = 169
base = √169
base = 13 yards

Now we can find the height using the previously given relationship:

height = 4 * base
height = 4 * 13
height = 52 yards

Therefore, the base of the triangle is 13 yards and the height is 52 yards.

To find the height and base of the triangle, we can use the formula for the area of a triangle:

Area = (1/2) * base * height

However, in this case, we are given the area and the relationship between the height and base. Let's use this information to find the height and base:

Given:
Area = 338 square yards
Height = 4 times the base

We need to set up an equation using these values and solve for the unknowns (height and base).

Let's represent the base as "b" and the height as "h":

Area = (1/2) * b * h
338 = (1/2) * b * 4b
338 = 2b^2

Now, let's isolate "b" by dividing both sides of the equation by 2:

338/2 = b^2
169 = b^2

To find the value of "b," we can take the square root of both sides of the equation:

b = √169
b = 13

Now, let's substitute the value of "b" back into the equation to find the height:

Height = 4 * base
Height = 4 * 13
Height = 52

Therefore, the base of the triangle is 13 yards and the height is 52 yards.