Question

PLEASE HELP !!!!!! I DONT UNDERSTAND SO PLEASE SOMONE AT LEAST HELP OR TRY!!!!.

In trapezoid EFGH, EF and HG are the bases. Point J is the midpoint of EHand point K is the midpoint of FG EF=5x+3 , HG=12x−3 , and JK=34 .


What is the value of x?


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In rectangle FGHJ , the diagonals intersect at point M, FM=3.2x , and JG=40 .


What is the value of x?


Enter your answer as a decimal in the box.

Answer 1

The first x = 4

The second x = 6.25

Explanation:

For the first question. We need to make use of the midsegment theorem which says, if you have a trapezoid with base1 and base2, then the midsegment is given as:

(Base1 + Base 2)/2.

We are given Base 1 = 5x + 3 and Base 2 = 12x – 3 and the midsegment, JK = 34. To find x we have:

(5x + 3 + 12x – 3)/2 = 34

This gives: 17x/2 = 34.

Therefore, x = (34 x 2)/17 = 4. Thus, x = 4.

As for the second question, we have two diagonals of the rectangle, FH and JG. We are given that JG = 40. We know that the diagonals of the rectangle are equal, therefore FH = 40 as well.

We are told that M is the midpoint, meaning FM is half of the diagonal FH. Mathematically this can be written as:

FM = FH/2

Given that FM = 3.2x and FH = 40, we have:

3.2x = 40/2

3.2x = 20

x = 20/3.2

x = 6.25