"The base of a triangle is five times its height. Its area is 160 square inches. Find the height and base, then enter their sum below."

Yall I'm so confused by this, if I could get some help that would be great!! Thank you!

b = base

h = height

Area of triangle:

A = b ∙ h / 2

In this case:

b = 5 h , A = 160 in²

160 = 5 h ∙ h / 2

160 = 5 h² / 2

Multiply both sides by 2

320 = 5 h²

Divide both sides by 5

64 = h²

h = ± √64

h = ± 8

Height can not be negative so:

h = 8 in

b = 5 h

b = 5 ∙ 8 = 40 in

Thank you! So you're saying that the sum is 40?

Not the sum is used for the area of a triangle, but half the product of two numbers.

The product of 5 and 8 is 40.

How would I calculate the sum?

"sum" means you add

8+40 = 48

Well, first of all, let me reassure you that triangles can be a bit confusing, but we'll figure this out together! Now, let's decipher this triangle riddle.

Let's call the height of the triangle "h" (because "h" stands for "height"), and since the base is five times the height, we can call the base "5h."

The area of a triangle can be found using the formula: Area = (1/2) * base * height.

So, if we plug in the values, we have 160 = (1/2) * 5h * h.

To simplify this equation, let's multiply 5h and h: 160 = (5/2) * h^2.

Now, multiply both sides of the equation by 2/5 to get rid of the fraction: (2/5) * 160 = (5/2) * (2/5) * h^2.

After simplifying, we get 64 = h^2.

Now, take the square root of both sides, and we find that the height, h, is ±8. But since the height of a triangle can't be negative, we'll take the positive value as the height.

So h = 8.

Now, to find the base, we multiply the height by 5: 5h = 5 * 8 = 40.

Finally, to find the sum of the height and base, we add them together: 8 + 40 = 48.

So, the sum of the height and base is 48 inches.

Hope that clears things up for you! Keep calm and solve triangles!

To solve this problem, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

Let's break down the given information:

1. The base of the triangle is five times its height.
We can represent the height as "h" and the base as "5h".

2. The area of the triangle is 160 square inches.
So, we have: 1/2 * 5h * h = 160

Now, let's solve for the height and base:

1/2 * 5h^2 = 160

Multiply both sides of the equation by 2 to get rid of the fraction:

5h^2 = 320

Divide both sides of the equation by 5:

h^2 = 64

Take the square root of both sides:

h = ±√(64)

Since we're looking for a positive value for the height, h = √(64) = 8.

Now that we know the height, we can find the base:

Base = 5h = 5 * 8 = 40

To find the sum of the height and base:

Sum = height + base = 8 + 40 = 48

Therefore, the sum of the height and base is 48.