Lucas is designing a flower garden in the shape of an isosceles right triangle. He has created a scale diagram. The lengths of the perpendicular sides in the scale diagram are 7 cm, and the hypotenuse of the real garden will be 3 m long. What is the area of the real garden? A. 450 B. 2.25 C. 1033 D. 4.5. 3. Which statement ...
To find the area of the real garden, we can use the scale ratio between the scale diagram and the real garden.
The scale ratio is given by 7 cm : 3 m. To find the conversion factor, we need to convert either centimeters to meters or meters to centimeters. Let's convert centimeters to meters:
1 cm = 0.01 m
So, the conversion factor is 0.01.
Now, we can find the length of the perpendicular sides in the real garden:
7 cm * 0.01 = 0.07 m
Therefore, the length of the perpendicular sides in the real garden is 0.07 m.
Next, we can use the formula for the area of a right triangle:
Area = (base * height) / 2
Since the triangle is isosceles, the base and height are the same length, which is 0.07 m.
Plugging the values into the formula:
Area = (0.07 * 0.07) / 2
Area = 0.0049 / 2
Area = 0.00245 square meters
Therefore, the area of the real garden is 0.00245 square meters.
The correct answer is not provided in the options.
To find the area of the real garden, we first need to find the lengths of the sides in the real garden.
According to the scale diagram, the lengths of the perpendicular sides are 7 cm. Let's assume that the scale is 1 cm = x meters, where x is the conversion factor from centimeters to meters.
So, the actual lengths of the perpendicular sides will be 7x meters.
The hypotenuse in the scale diagram is 3 m, which means the actual length of the hypotenuse in the real garden is 3 meters.
Since we have an isosceles right triangle, the two perpendicular sides have the same length in the real garden. So, we can set up the equation:
7x = 3
To solve for x, divide both sides of the equation by 7:
x = 3/7
Now, we can find the length of each perpendicular side in the real garden:
Perpendicular side length = 7x = 7 * (3/7) = 3 meters
Next, we can calculate the area of the real garden using the formula for the area of a right triangle: A = 1/2 * base * height
In an isosceles right triangle, the base and height are the same length, so we can set up the equation:
Area = 1/2 * (3 meters) * (3 meters) = 4.5 square meters
Therefore, the area of the real garden is 4.5 square meters.
So the answer to the question is D. 4.5 square meters.
the area of an isosceles right triangle is one half the square of the hypotenuse
a = 3² / 2