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The length of CE, the diagonal of rectangle DEFG, can be calculated using Pythagorean theorem on triangle CEF. This gives CE = √[(72) + (172)] = approximately 18.38 cm.
According to the problem, rectangles ABCD and DEFG are congruent. This means that their corresponding sides are equal. So, the side AD in rectangle ABCD is equal to side EF in rectangle DEFG.
Given, AD = 17 cm. Hence EF (which is the same length as AD in the congruent rectangle) is also 17 cm.
You're asked to find the length of CE, which is the diagonal of rectangle DEFG. If we look closely, the triangle CEF is a right triangle with CE being the hypotenuse.
We can apply the Pythagorean Theorem which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Namely, in this context, CE2 = CF2 + EF2 = (72) + (172) = 49+289 = 338.
So, CE = √338 = approximately 18.38 cm.
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The length of CE is found by taking the difference of the lengths of DE and CD, which are sides of congruent rectangles. Since DE is 17 cm and CD is 7 cm, the length of CE is 10 cm.
The rectangles ABCD and GDEF are given as congruent, which means all corresponding sides and angles are equal.
Since the rectangles are congruent and all points correspond, side AD is congruent to side GE. If AB is 7 cm and AD is 17 cm, we can deduce that GD is also 17 cm since AB corresponds to GF and AD to GE in the congruent rectangle GDEF.
As per the problem, CE is the difference between DE and CD, and we know that in congruent figures corresponding sides are equal, so CD is also 7 cm.
Consequently, CE is the difference of DE (which equals AD or 17 cm) and CD (which equals AB or 7 cm).
So, CE = DE - CD, which simplifies to CE = 17 cm - 7 cm, resulting in CE being equal to 10 cm.
