Consider a rectangle whose length, L, is 4 more than twice its width, w. a. Write an expression for L in terms of w. b. Show that the perimeter, P, is equal to = 6 + 8. c. Given the perimeter is 20, find the length and width of the rectangle using your answer to part b.
Mathematics · High School · Thu Feb 04 2021
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According to the question, Consider length=L and width=W
given that: length is 4 more than twice its width
1.Write an expression for L in terms of w
so, L=2W+4
2.Show that the perimeter, P, is equal to = 6w + 8
perimeter, P = 2(L+W)
=2(2W+4+W) (* L=2W+4)
=2(3W+4)
P =6W+8
hence prove that P =6W+8
3. if perimeter is 20, find the length and width of the rectangle
P=2(L+W) above we find the perimeter, we can apply this here:-
20=6W+8
20-8=6W
12=6W
W=12/6
W=2
width is 2 put this value in equation L=2W+4
L(length)=2*2+4
=4+4
=8
so length = 8 and width= 2