Question

Catherine is creating a triangular banner for her school's football team. She wants the height of the banner to be 4 times as tall as the width of the base of the triangle. If she wants the total area of the banner to be 8 feet squared (8ft2), how wide should the base of the triangle be in feet?

Answer 1

The base of the triangle should be 2 feet

Explanation:

Let the base of the triangle be y

She wants the height of the banner to be 4 times as tall as the width of the base of the triangle

So height is =
`4 * y` = 4y

Now we know that the area of the triangle is =
`(1)/(2) (base * height)`

we also know that total area of the banner is 8 feet squared

Then

`8 = (1)/(2)(y * 4y)`

`8 = (4y^2)/(2)`

`16 = 4y^2`

`(16)/(4) = y^2`

`4 = y^2`

`y = √(4)`

y = 2

Width if the base of the triangle is 2 feet