Question

A right triangle's height is 3 times the length of its base. if the area of the triangle is 726 cm^2, what is the height

Answer 1

Let the length of the base be x.

Height = 3x

Area = 726


`(1)/(2) bh` = 726


`(1)/(2)* 3x*x` = 726


`3 x^(2)` = 1452


`x^(2)` = 484

x = 22.

Hence,

The length of the base is 22 cm.

The height of the triangle is 66 cm.

Answer 2

22 cm is the height of the right triangle .

Explanation:

Area of the triangle = A =
`726 cm^2`

Let the base 'b' of the triangle be x

A right triangle's height 'h' is 3 times the length of its base we can also be written as:

= h = 3x

Area of the triangle =
`(1)/(2)b* h`

`A=(1)/(2)b* h`

`726 cm^2=(1)/(2)* x* 3x`

`x^2=(726 cm^2* 2)/(3)`

`x=22 cm`

Height of the right triangle = h = 3x = 3 × 22 cm = 66 cm