Question

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

Answer 1

Answer:

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

Step-by-step 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:

$Area=\frac{1}{2} \times base\ \times height\\\\15=\frac{1}{2} \times (3x-9)\times x\\\\15=\frac{3x^2-9x}{2}$

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:

$3x-9\\\\=3\times 5-9\\\\=15-9\\\\=6\ cm.$

Hence, the base is 6cm.

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