Question

Can someone please help me with finding X(Round to nearest tenth),Y and the perimeter?

(Geometry)

Answer 1

A: x = 9 4/7

B: y = 15

C: P = 95 units

Explanation:

You want the values of x and y, and the perimeter of the isosceles trapezoid ABCD with AB=20, CD=2y-10, AD=15, BC=40, AD║CB, angle A=10x-22, and angle C=4x+68.

Part A

The value of x can be found using the fact that base angles are congruent and the sum of angles on one side of the trapezoid is 180°.

∠A +∠C = 180

(10x -22) +(4x +68) = 180 . . . . . use the given angle expressions

14x +46 = 180 . . . . . . . . . . . . simplify

14x = 134 . . . . . . . . . . . . . . subtract 46

x = 134/14 = 9 4/7 . . . . divide by 14

The value of x is 9 4/7.

Part B

Sides of the isosceles trapezoid are congruent

CD = AB

2y -10 = 20 . . . . . substitute the given lengths

2y = 30 . . . . . . add 10

y = 15 . . . . . divide by 2

The value of y is 15.

Part C

The perimeter is the sum of the side lengths.

P = AB +BC +CD +AD

P = 20 +40 +20 +15 = 95

The perimeter is 95 units.

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Additional comment

The expressions for the angles and the value of x are impossible in this figure. For the found value of x, angle A is 73 5/7°, and angle C is 106 2/7°. The angle adjacent to the short base will be obtuse, so these are impossible measures.

For the given side lengths, angle A is 128.7°, and angle C is 51.3° (using trigonometry).

Answer 2

x = 9.5

y = 15

Explanation:

The sum of angles A and C is equal to 180° because they are supplementary angles:

10x - 22 + 4x + 68 = 180 add like terms

14x + 46 = 180 subtract 46 from both sides

14x = 134 divide both sides by 14

x = 9.5 approximately

The perimeter is calculated by adding all side lengths up:

AB + CD + AD + BC

AB = AC because this is an isosceles trapezoid

20 + 20 + 15 + 40 = 95

CD is equal to 20 so the value of y:

2y - 10 = 20 add 10 to both sides

2y = 30 divide both sides by 2

y = 15