A triangle has an area of $29.7 cm^2$ and a base of 13.5 cm. Use the formula $A=\frac{1}{2} b h$ to find the height.
A. $h=4.2 cm$
B. $h=4.7 cm$
C. $h=4.1 cm$
D. $h=4.4 cm$
Answer (2)
Substitute the given area and base into the triangle area formula.
Multiply both sides of the equation by 2 to eliminate the fraction.
Divide both sides by the base to isolate the height.
Calculate the height: 4.4 c m
Explanation
Problem Analysis We are given the area of a triangle A = 29.7 c m 2 and its base b = 13.5 c m . We need to find the height h using the formula A = 2 1 bh .
Substitute Values Substitute the given values into the formula:
29.7 = 2 1 ( 13.5 ) h
Multiply by 2 To solve for h , first multiply both sides of the equation by 2:
2 × 29.7 = 2 × 2 1 ( 13.5 ) h
59.4 = 13.5 h
Isolate h Now, divide both sides by 13.5 to isolate h :
h = 13.5 59.4
Calculate h Calculate the value of h :
h = 4.4
Final Answer Therefore, the height of the triangle is 4.4 cm.
Examples
Understanding how to calculate the height of a triangle given its area and base is useful in many real-world scenarios. For example, architects use this formula to calculate roof heights, and construction workers use it to determine the amount of material needed for triangular structures. Landscape designers might use it to plan the layout of a garden with triangular flower beds. Knowing the relationship between area, base, and height allows for precise planning and efficient use of resources in various fields.
The height of the triangle is found to be 4.4 cm using the area and base values provided. We used the formula for the area of a triangle to derive the height. The correct answer is option D: h = 4.4 c m .
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