Question

Tan is designing a Japanese rock garden in the shape of a right triangle so that the second- shortest side is twice the length of the shortest side. The area of the garden must be `30 m^2`. What are the three sides of his garden?

Answer 1

The three sides of Tan's garden must be `5.477m, 10.95m and 12.247m`

Explanation:

Japanese rock garden is in the shape of a right triangle.
Let the length of the shortest side (base) be `x`
So, the second- shortest side (height) is twice the length of the shortest side, i.e. `2x`.
The area of the garden = `30m^2`

What are the three sides of his garden?

Area of triangle = `1/2 base \times height`

`30 = 1/cancel2\times x\times cancel2x`

`30 = x^2`

So, `x= sqrt30 ~~5.477`------(truncated value)

So the three sides are :

`x~~ 5.477 m`

`2x ~~ 10.95 m`

`(Hypoten` `use)^2 ~~ (5.477)^2 + (10.95)^2`

`(Hypoten` `use)^2 ~~ 149.900029~~ 150 m`

`therefore (Hypoten` `use) ~~ 12.247 m`

The three sides of Tan's garden must be `5.477m, 10.95m and 12.247m` (approximately).