Jordana was shown this diagram of an isosceles trapezoid and its reduction. She was asked to find the perimeter of the reduced trapezoid. Her work is shown below.
30 cm
A
12 cm
4 cm
B
36 cm
Figures not drawn to scale.
Scale factor
Jordana's Work
4.
123
Side A
30x3 =10
Side B
30 x
10
3
Perimeter
10+ 10+4+4 = 28

The question is unclear to me, 30x3=10 WHAT, 30x3=90 not 10

And also it seems you already know the answer Perimeter=28cm

C.

Step-by-step explanation:

Jordana made a mistake when she calculated the length of side B.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4