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Answer:
The height is <u>6 cm</u> and the base is <u>5 cm</u>.
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
And then base of the triangle =
The area of the triangle =
Now, we put formula to get the base and height of the triangle:
<em>Multiplying both sides by 2 we get:</em>
<em /><em />
<em /><em />
<em>Dividing both sides by 3 we get:</em>
<em /><em />
<em>Subtracting both sides by 10 we get:</em>
Now, solving the quadratic equation:
Hence, the negative result is not to be taken so, we take the positive result.
<u><em>Thus, the height is 5 cm.</em></u>
Now, substituting the value of to get the base:
<u><em>Hence, the base is 6cm.</em></u>
Therefore, the height is 6 cm and the base is 5 cm.