Can someone help me with this?
ABCD is a rectangle. AD = x + 10, BC = 2x + 8 and CD = 5. Solve for BD.
I love problems like this.
Draw out a diagram.
Also, use the Pythagorean Theorem.
To solve for BD in the rectangle ABCD, we can use the Pythagorean Theorem which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider triangle BCD as a right triangle. The sides BC and CD are known, BC = 2x + 8 and CD = 5, and we need to solve for the length of BD.
Using the Pythagorean Theorem, we have:
BD^2 = BC^2 + CD^2
Substituting the given values, we have:
BD^2 = (2x + 8)^2 + 5^2
Simplifying the equation, we get:
BD^2 = (4x^2 + 32x + 64) + 25
BD^2 = 4x^2 + 32x + 89
To solve for BD, we take the square root of both sides of the equation:
BD = sqrt(4x^2 + 32x + 89)
So, BD is equal to the square root of 4x^2 + 32x + 89.