Question

Analyze the diagram below and complete the instructions that follow.

3
4
45°
х
Find the value of x and the value of y.
A. X-4, 7-8
B. x - 7,7=43
C. x = 4√3, 7-72
D. x=753, y = 4√2

Answer 1

`x= 7, y=4√(2)`

Correct option B.

Explanation:

The diagram shows a trapezoid with a base angle of 45° and the other base angle of 90°.

We have completed the diagram to draw a perpendicular line over the base of height h=4. A triangle is formed with an angle of 45°.

Recall a right triangle with angles of 45° is isosceles, thus the base and the height are h=4. Please check the diagram below.

For that triangle, we apply Pythagora's Theorem:

`y^2=4^2+4^2=2*4^2`

Thus:

`y=√(2*4^4)=4√(2)`

`y=4√(2)`

The base of the trapezoid x is h + 3 = 7

Thus:

`\mathbf{x= 7, y=4√(2)}`

Correct option B.