A scale drawing of a square has a side length of 9 inches. The drawing has a scale of 1 in. : 5 mi. Find the actual perimeter and area of the square.

Area = 2025 miles²

Perimeter = 180 miles

Step-by-step explanation:

Given the following :

Scale of drawing = 1 inch : 5 miles

Length of side of the scale drawing = 9 inches

To find The actual perimeter and area of the square, we need ;

Actual length of the drawing :

1 inch = 5 miles

9 inches = (5 × 9) miles = 45 miles

Hence,

Area of a square = a²

Where a = side length

Actual side length = 45 miles

Actual area of square = 45² = 2025 miles²

Actual Perimeter of square :

Perimeter of a square = 4a

a = side length

Actual perimeter = 4(45) = 180 miles

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).