Question

The height of a triangle is 5 m less than its base. The area of the triangle is 42 mº

What is the length of the base?
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Answer 1

Length of base of triangle = 12 meters

Explanation:

Let the base of the triangle be =
`x` meters

The height of triangle is 5 less than its base.

So, height of the triangle is given by =
`x-5`

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

⇒
`((1)/(2) * x* (x-5))\ m^2`

⇒
`(x^2-5x)/(2)\ m^2` [Using distribution.]

Area of triangle given =
`42\ m^2`

Thus we have:

`(x^2-5x)/(2)=42`

Multiplying both sides by 2 to remove fraction.

`2*(x^2-5x)/(2)=42* 2`

`x^2-5x=84`

Subtracting both sides by 84.

`x^2-5x-84=84-84`

`x^2-5x-84=0`

We can now solve quadratic using formula.

`x=(-b\pm√(b^2-4ac))/(2a)`

Plugging in values from the quadratic equation to solve for
`x`

`x=(-(-5)\pm√((-5)^2-4(1)(-84)))/(2(1))`

`x=(5\pm√(25+336))/(2)`

`x=(5\pm√(361))/(2)`

`x=(5\pm19)/(2)`

So,

`x=(5+19)/(2)` and
`x=(5-19)/(2)`

`x=(24)/(2)` and
`x=(-14)/(2)`

`x=12` and
`x=-7`

Since length cannot be negative, we take
`x=12` meters as length of base of triangle. (Answer)