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3 years ago

You need to design a rectangle with a perimeter of 14.2 cm. The length must be 2.4 cm. What is the width of the

Mathematics

1 answer:

irina1246 [14]3 years ago

4 0

Part (a)

<h3>Answer: 2(2.4+w) = 14.2</h3>

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Explanation:

L = 2.4 = length

W = unknown width

The perimeter of any rectangle is P = 2(L+W)

We replace L with 2.4, and replace P with 14.2 to get 14.2 = 2(2.4+w) which is equivalent to 2(2.4+w) = 14.2

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Part (b)

<h3>Answer: w = 4.7</h3>

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Explanation:

We'll solve the equation we set up in part (a)

2(2.4+w) = 14.2

2(2.4)+2(w) = 14.2

4.8+2w = 14.2

2w = 14.2-4.8

2w = 9.4

w = 9.4/2

w = 4.7

The width must be 4.7 cm.

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7. Find: (i) x + y +z (ii) a+b+c+d

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Answer:

Q.1 360° Q.2 360°

Step-by-step explanation:

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70°+40°+a=180(by angle sum property)

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Q.2 let the fourth angle of the quadrilateral be x

120°+70°+60°+ x=360° (by angle sum property)

250°+x=360°

x=360°-250°

x=110°

angle a=120°+a=180°(by linear angle)

a=180°-120°

a=60°

angle b=70°+b=180°

b=180°-70°

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3 years ago

Calculate pqrst in the diagram above showing your solutions

Eva8 [605]

Answer:

a. p = 6

b. q = 4

c. r = 8

d. s = 10; t = 8.3

Step-by-step explanation:

1. a. The side length of two similar triangles are proportional, therefore:

$\frac{9}{p} = \frac{15}{10}$

Cross multiply

$15*p = 10*9$

$15*p = 90$

Divide both sides by 15

p = 6

b. Based on the midsegment theorem,

$q = \frac{1}{2}(8)$

$q = 4$

c. The side length of two similar triangles are proportional, therefore:

$\frac{4}{10} = \frac{r}{20}$

Multiply both sides by 20

$\frac{4}{10} \times 20 = \frac{r}{20} \times 20$

$\frac{80}{10} = r$

r = 8

d. The side length of two similar triangles are proportional, therefore:

$\frac{9 + 6}{9} = \frac{s}{6}$

$\frac{15}{9} = \frac{s}{6}$

Multiply both sides by 6

$\frac{15}{9} \times 6 = \frac{s}{6} \times 6$

$\frac{15 \times 6}{9} = s$

s = 10

$\frac{9 + 6}{9} = \frac{t}{5}$

$\frac{15}{9} = \frac{t}{5}$

Multiply both sides by 5

$\frac{15}{9} \times 5 = \frac{t}{5} \times 5$

$\frac{15 \times 5}{9} = t$

t = 8.3 (nearest tenth)

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