Question

The base of a triangle is 9cm less than the three times the height. The area is 15 cm2.

Find the height and base.

Answer 1

The height is 6 cm and the base is 5 cm.

Explanation:

Given:

The base of a triangle is 9 cm less than the three times the height. The area is 15 cm².

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

Let the height of the triangle be
`x.`

And then base of the triangle =
`3x-9.`

The area of the triangle =
`15\ cm^2.`

Now, we put formula to get the base and height of the triangle:

`Area=(1)/(2) * base\ * height\\\\15=(1)/(2) * (3x-9)* x\\\\15=(3x^2-9x)/(2)`

Multiplying both sides by 2 we get:

`30=3x^2-9x`

`30=3(x^2-3x)`

Dividing both sides by 3 we get:

`10=x^2-3x`

Subtracting both sides by 10 we get:

`0=x^2-3x-10\\\\x^2-3x-10=0`

Now, solving the quadratic equation:

`x^2-5x+2x-10=0\\\\x(x-5)+2(x-5)=0\\\\(x-5)(x+2)=0\\\\\\x-5=0\ \ \ \ \ x+2=0\\\\x=5\ \ \ \ \ \ \ \ \ \ x=-2`

Hence, the negative result is not to be taken so, we take the positive result.

Thus, the height is 5 cm.

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

`3x-9\\\\=3* 5-9\\\\=15-9\\\\=6\ cm.`

Hence, the base is 6cm.

Therefore, the height is 6 cm and the base is 5 cm.