Question

A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of te triangle is 16m to the power of 2, what are the base and height of the triangle

Answer 1

The base of triangle is
`(8)/(√(3)) \ m` and the height of triangle is
`(12)/(√(3)) \ m.`

Explanation:

Given:

A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of the triangle is 16m to the power of 2.

Now, to find the base and height of the triangle.

The base of triangle =
`x*(1)/(2) =(x)/(2) \ m.`

The height of triangle =
`x* (3)/(4) =(3x)/(4)\ m.`

The area of triangle =
`16\ m^2.`

Now, we put the formula of area to solve:

`Area=(1)/(2) * base* height`

`16=(1)/(2) * (x)/(2) * (3x)/(4)`

`16=(3x^2)/(16)`

Multiplying both sides by 16 we get:

`256=3x^2`

Dividing both sides by 3 we get:

`(256)/(3) =x^2`

Using square root on both sides we get:

`(16)/(√(3))=x`

`x=(16)/(√(3))`

Now, by substituting the value of
`x` to get the base and height:

`Base=(x)/(2)\\\\Base=((16)/(√(3)))/(2) \\\\Base=(8)/(√(3)) \ m.`

So, the base of triangle =
`(8)/(√(3)) \ m.`

`Height=x*(3)/(4) \\\\Height=(16)/(√(3))* (3)/(4) \\\\Height=(12)/(√(3)) \ m.`

Thus, the height of triangle =
`(12)/(√(3)) \ m.`

Therefore, the base of triangle is
`(8)/(√(3)) \ m` and the height of triangle is
`(12)/(√(3)) \ m.`