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sergejj [24]
3 years ago
9

The perimeter of a rectangle is dependent on the length of each of its sides. Suppose the base of a rectangle is two more than i

ts height. Write an equation to represent the perimeter as a function of its height.
Mathematics
1 answer:
Bezzdna [24]3 years ago
4 0
Perimeter=4h+4

If the base is 2 more than the height, it gives us the equation:
b=h+2

The equation for the perimeter of a rectangle can be though of as 2b+2h, so substituting in (h+2) for b from the first equation, we get 2(h+2)+2h.

This can be simplified to be 2h+4+2h or 4h+4
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<h2>Answer and Explanation to questions 13,14,15</h2>

13) \mathbf{\overline{XY}\cong\overline{CD}}        as given in the question.

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15) \mathbf{\overline{CD}\cong\overline{YZ}}

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<h2>Answer and Explanation to questions 16,17,18</h2>

∠3 is supplementary to ∠1 means: ∠3 + ∠1 = 180°

And, according to figure ∠1 + ∠2 = 180° as ∠1 and ∠2 form a straight line.

∠3 + ∠1 = 180°    .............(i)

∠1 + ∠2 = 180°    .............(ii)

subtracting equation (i) and (ii) will give ∠3 = ∠2   ..........(iii)

15) ∠3 is supplementary to ∠1                        as given in the question

16) ∠2 is supplementary to ∠1                        as shown be equation (ii)

18) ∠3 ≅ ∠2                                                      as shown by equation (iii)

<h2>Answer and Explanation to questions 19</h2>

∠3 and ∠4 form a straight line. Therefore, ∠3 + ∠4 = 180°   .......(i)

∠4 and ∠5 form a straight line. Therefore, ∠4 + ∠5 = 180°   .......(ii)

subtracting equation (i) and (ii)

∠3 + ∠4 - (∠4 + ∠5) = 180°-(180°)

∠3 + ∠4 - ∠4 - ∠5 = 180°-180°

∠3 - ∠5 = 0

∴ ∠3 = ∠5     (Hence Proved)

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