Given: abcd is rectangle, e ∈ ac, ac = ce = 5 in, be = 7 in.
find: ed =?
aedcb = ?

ed =__ in.
area= __ sq. in

Step-by-step explanation:

The key to solving this problem is to recognize that the horizontal distance from AD to E is 2×AB, and the vertical distance from AB to E is 2×BC.* This gives rise to two equations using the Pythagorean theorem:

Subtracting the first equation from the second, we get ...

  (AB² +4×BC²) -(AB² +BC²) = 49 -25

  3×BC² = 24

  BC = √(24/3) = √8

Then ...

  AB² = 25 -8 = 17

  AB = √17

__

The length ED is also found using the Pythagorean theorem:

  ED² = (2×AB)² +BC² = 4×17 + 8 = 76

  ED = √76

  ED = 2√19 . . . inches

__

The area of triangle EDC is ...

  A(EDC) = (1/2)AB×BC

and the area of triangle ECB is ...

  A(ECB) = (1/2)BC×AB

So the area of EDCB is the sum ...

  A(EDCB) = A(EDC) +A(ECB)

  = (1/2)AB×BC +(1/2)AB×BC = AB×BC

  = (√17)(√8)

  A(EDCB) = 2√34 . . . square inches

* You might be able to better see this if you translate rectangle ABCD so its diagonal AC is coincident with segment CE.

yes

step-by-step explanation: