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Read, analyze, and answer the items that follow. Refer to the figure at the right. Show your solution and indicate the properties you applied to justify each step on your answer sheet. You may illustrate each given to serve as your guide. W H a. If W1 = 6y + 6 and HS = 2y + 26, how long is HS? b. Quadrilateral WISH is a rectangle, and its perimeter is 112 centimeters. Side WI is 10 centimeters less than twice the other side. What are its dimensions and how large is its area?​

Sagot :

Answer:

a. The opposite sides in a rectangle are congruent; hence,

[tex]WI=HS[/tex]

[tex]6y+6=2y+26[/tex]

[tex]6y-2y=26-6[/tex]

[tex]4y=20[/tex]

[tex]y=5[/tex]

[tex]HS=2y+26=2(5)+26=36[/tex]

b. Let x be the length of the other side

[tex]WI=2x-10[/tex]

The perimeter of a rectangle is twice the sum of its length and width.

[tex]P=2(L+W)[/tex]

[tex]2(x+2x-10)=110[/tex]

[tex]3x-10=55[/tex]

[tex]x=\frac{55+10}{3}=21.67cm[/tex]

[tex]WI=2x-10=2(21.67)-10=33.33cm[/tex]

[tex]A=bh=21.67(33.33)=722.22cm^{2}[/tex]

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