Answer:
<h2>7x</h2>
Step-by-step explanation:
<h3><u>Part A: An equation to represent this situation, where x represents the original length of the rectangle is:</u></h3>
<h3><u>Part B: Original length of the rectangle is 12 inches</u></h3>
<em><u>Solution:</u></em>
Given that,
A rectangle has a width of 2.5
Therefore,
width = 2.5 inches
Let "x" be the original length of the rectangle
When the length of this rectangle is decreased by 5 inches
Therefore,
New length = x - 5
The new area of the rectangle is 17.5 square inches
Therefore,
<em><u>The area of rectangle is given as:</u></em>
Thus original length of the rectangle is 12 inches
Answer:
ΔGJH ≅ ΔEKF
HL: GH and EF
SAS: FK and JH (or GH and EF)
ASA: ∠JGH and ∠FEK (or ∠EFK and ∠JHG)
ΔGFJ ≅ ΔEKH
SSS: KH and FJ
SAS: ∠KEH and ∠FGJ
Step-by-step explanation:
List whatever angles/sides need to be congruent for the two triangles to be congruent.
Prove ΔGJH ≅ ΔEKF using....
- HL (Hypotenuse + Leg)
We already have two legs that are congruent (EK and GJ), so we just need the hypotenuses (GH and EF) to be equal.
- SAS (Side + Angle + Side)
1 pair of sides (EK and JG) are equal, and m∠EKF = m∠GJH. So we need one more side. You can either use FK and JH or GH and EF.
- ASA (Angle + Side + Angle)
1 pair of angles (∠EKF and ∠GJH) are already given as equal, and 1 pair of sides (EK and GJ) are equal. We just need one more pair of angles. So either ∠JGH and ∠FEK or ∠EFK and ∠JHG.
Prove ΔGFJ ≅ ΔEKH using...
- SSS (Side + Side + Side)
Two pairs of sides (EK + GJ and EH + FG) are equal, so KH and FJ need to be equal.
- SAS (Side + Angle + Side)
FG + EH and KE + GJ are equal. We need to use the angle in between them to use SAS, so ∠KEH and ∠FGJ need to be equal.
Answer:
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Step-by-step explanation:
