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

(Geometry)

Can someone please help me with finding X(Round to nearest tenth),Y and the perimeter-example-1
User Jjczopek
by
2.7k points

2 Answers

17 votes
17 votes

Answer:

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.

__

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).

User Evans Belloeil
by
3.1k points
20 votes
20 votes

Answer:

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

User Kresimir
by
2.8k points
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