Mathematics, 26.08.2019 22:00 bm42400

Rectangle 1 has length x and width y. rectangle 2 is made by multiplying each dimension of rectangle 1 by a factor of k, where k > 0.
(a) are rectangle 1 and rectangle 2 similar? why or why not?
(b) write a paragraph proof to show that the perimeter of rectangle 2 is k times the perimeter of rectangle 1.
(c) write a paragraph proof to show that the area of rectangle 2 ismtimes the area of rectangle 1.

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(a) The Rectangles are similar because all angles of all rectangles are equal to 90°. Then, the corresponding sides have the equivalent ratio equal to k.
(b) The perimeter of the rectangle is the sum of the measurements of all sides. Such that for Rectangle 1, it should be.
Perimeter (Rectangle 1) = 2x + 2y
Then for rectangle 2,
Perimeter (Rectangle 2) = 2kx + 2ky = k (2x + 2y)
= k(Perimeter of rectangle 1)

c. Area of rectangle is the product of the lengths of two sides, (x)(y). For Rectangle 2, that would be (kx)(ky) = k²xy

Answer from: PNA

(a) Rectangle 1 and Rectangle 2 are similar rectangles because the lengths of their respective sides are proportional, and their four angles are equal.

(b) The perimeter of a rectangle is the sum of twice its base plus twice its height. For rectangle 1, the perimeter is P = 2x + 2y . For rectangle 2, the perimeter is 2kx + 2ky = k (2x + 2y) = kP .

(c) The area of a rectangle is the product between the value of its base and its height. For rectangle 1, the area is A = xy . For rectangle 2, the area is (kx) (ky) = k ^ 2 (xy) = k ^ 2A .

Step-by-step explanation:

Answer from: Quest

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

Answer from: Quest

40 minutes

step-by-step explanation:

add the time and multiply by 2

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