Question

Analyze the diagram below and complete the instructions that follow.
7
y
450
X
Find the value of x and the value of y.
A. x = 16, y = 9V2
B. x = 7, y = 16 V2
C. x= 16V/, y = 7.12
D. x= 7/3, y = 16

Answer 1

Answer:

$A.\ ~~x=16,~ y=9\sqrt{2}$

Step-by-step explanation:

We have completed the diagram with some lengths that come directly from the figure's symmetry.

Note the triangle formed at the left side of the trapezium is isosceles because it has an angle of 90° and another angle of 45°.

This means the base of the triangle has the same length as the height of 9.

This means the total base of the trapezium is x = 9 + 7 = 16

The right triangle must satisfy Pythagora's Theorem:

$y^2=9^2+9^2$

$y^2=2*9^2$

$y=\sqrt{2*9^2}$

Simplifying the radical:

$y=9\sqrt{2}$

The correct answer is: $\mathbf{A.\ ~~x=16,~ y=9\sqrt{2}}$