a triangle whose base is 18 inches long has an area of 280 square inches. find the area of a similar triangle whose base is 6 1/4 feet long.
the area is proportional to the square of the side length
280 / (18^2) = A / (6 1/4)^2
4861 sq.in
To find the area of the similar triangle, we need to understand the relationship between the areas of similar geometric shapes.
Two triangles are considered similar if their corresponding sides are in proportion. In this case, we are given that the two triangles have bases in the ratio of 18 inches to 6 1/4 feet. To compare these lengths, we need to convert the feet to inches.
1 foot = 12 inches
So, 6 1/4 feet = 6 × 12 + 1/4 × 12 = 72 + 3 = 75 inches
Now, we can set up the ratio of the bases:
18 inches / 75 inches = x (similar triangle base) / 75 inches
Simplifying this equation, we get:
18 / 75 = x / 75
To find the value of x, we can cross-multiply and solve for x:
18 × 75 = 75 × x
1350 = 75x
x = 1350 / 75 = 18
Now that we know the ratio of the bases is 18:75, we can find the ratio of the areas.
The area of a triangle is given by the formula: A = (base × height) / 2
Let's assume the height of the first triangle is h1. We can write:
280 = (18 × h1) / 2
Simplifying this equation, we get:
h1 = 2 × (280 / 18) = 2 × (140 / 9) = 280 / 9 ≈ 31.11 inches
Now, let's find the height of the second triangle, h2, using the ratio of bases:
h1 / 18 = h2 / 75
Rearranging the equation to find h2, we get:
h2 = (h1 × 75) / 18 = (31.11 × 75) / 18 ≈ 129.79 inches
Finally, we can find the area of the second triangle using the formula:
A2 = (base × height) / 2
A2 = (75 × 129.79) / 2 = 4856.25 square inches
Hence, the area of the similar triangle with a base of 6 1/4 feet is approximately 4856.25 square inches.