It is given that, B ≅ BC and AD ≅ CD
We need BD perpendicular to AC, then only we can say triangles AXB and CXB are congruent using the HL theorem.
If BD perpendicular to AC, means that AB and CB are the hypotenuse of triangles AXB and CXB respectively.
from the given information ABCD is a square
If BD and AC bisect each other then AX = CX
Then only we can immediately possible to prove that triangles AXD and CXD are congruent by SSS congruence theorem
x^2 +7x +10
when factored becomes
(x+2) (x+5)
the zeros are x +2 = 0, x = -2
x +5 = 0 x = -5
zeros are -2 and -5
Petra can make 8 costumes with 12 yards of fabric
<h3><u>Solution:</u></h3>
Given that Petra was given 12 yards of fabric to make costumes for the school play
Each costume requires
yards
<em><u>To find: number of costume Petra can make</u></em>
The number of costume Petra can make is calculated by dividing the total fabric she has by fabric needed for one costume

Total fabric she has = 12 yards
Fabric needed for 1 costume =
yards
Therefore,

Thus petra can make 8 costumes with 12 yards of fabric