Final answer:
To solve for the height and base of the triangle with an area of 33 cm², where the base is 5 cm wider than the height, use the area formula 1/2 × base × height to establish a quadratic equation. By solving the equation, we find the height to be 6 cm and the base to be 11 cm.
Step-by-step explanation:
The question involves solving for the dimensions of a triangle when the area is known. The problem states that the triangle is 5 cm wider than it is tall. We are given that the area of the triangle is 33 cm². To find the height and base, we can use the formula for the area of a triangle, which is 1/2 × base × height.
Let the height of the triangle be 'h' cm. According to the question, the base will then be 'h+5' cm. Using the area formula, we get 1/2 × (h+5) × h = 33. Multiplying both sides by 2 to get rid of the fraction, we have (h+5) × h = 66. This simplifies to a quadratic equation h² + 5h - 66 = 0. By solving this equation, we can find the value of 'h' and subsequently 'h+5'.
Using the quadratic formula or factoring, we find that the positive solution for 'h' is 6 cm. Therefore, the base 'h+5' will be 11 cm. So, the height is 6 cm and the base is 11 cm.