Point X is on side BC of rectangle ABCD. If AX = 5 units, XD = 12 units, and AD = 13 units, find the area of ABCD.
Well, let's take a closer look at this rectangle ABCD. Did you know that rectangles are known for their right angles? They're like the squares' way cooler cousin. Anyway, back to the problem.
Since AX = 5 units and XD = 12 units, we can see that AD is the sum of those two lengths, which is 5 + 12 = 17 units. Now, we have the length of one side of the rectangle.
Since ABCD is a rectangle, that means AD is also the length of the opposite side. So we have the length (AD) and now we need to find the width of the rectangle.
We know that BC = AD - XD, which is 17 - 12 = 5 units. And since AB is the same length as CD (since it's a rectangle and all), we also have AB = XD = 12 units.
To find the area of ABCD, we simply multiply the length and width. So the area is 5 units (BC) multiplied by 12 units (AB or CD), which gives us 60 square units.
So, the area of the rectangle ABCD is 60 square units.
To find the area of rectangle ABCD, we need to find the length of side BC.
Since AX = 5 units and XD = 12 units, we can calculate the length of AD using the Pythagorean theorem:
AD^2 = AX^2 + XD^2
AD^2 = 5^2 + 12^2
AD^2 = 25 + 144
AD^2 = 169
Taking the square root of both sides, we find:
AD = √169
AD = 13 units
Since AD is the diagonal of the rectangle, it divides it into two congruent right triangles. Triangle ADB and triangle CDB are congruent.
Now, let's calculate the length of side BC. Since AD = 13 units, BC is the base of the right triangle ADB.
Using the Pythagorean theorem again:
BC^2 = AD^2 - BD^2
BC^2 = 13^2 - 5^2
BC^2 = 169 - 25
BC^2 = 144
Taking the square root of both sides, we find:
BC = √144
BC = 12 units
Now that we know the length of side BC, we can calculate the area of the rectangle by multiplying the length BC by the width AD.
Area of ABCD = BC * AD
Area of ABCD = 12 units * 13 units
Area of ABCD = 156 square units.
Therefore, the area of rectangle ABCD is 156 square units.
To find the area of rectangle ABCD, we need to know the length and width of the rectangle. However, from the given information, we only know the lengths of certain segments within the rectangle.
To determine the area of ABCD, we can use the fact that opposite sides of a rectangle are equal in length. Consequently, we can deduce that AD and BC are congruent.
Given that AD = 13 units, we can conclude that BC is also 13 units long.
Now, we have two adjacent sides of the rectangle:
AB = AD = 13 units
BC = 13 units
Since opposite sides of a rectangle are equal, we can infer that opposite sides AB and CD, as well as opposite sides BC and DA, are equal in length.
By using the lengths of AB and BC, we can calculate the area:
Area of ABCD = AB * BC = 13 units * 13 units = 169 square units.
Therefore, the area of rectangle ABCD is 169 square units.