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3 years ago

Can someone help me out with this question? (Example 1)

Mathematics

1 answer:

lora16 [44]3 years ago

8 0

Answer:

The answer to your question is:

x = 10

∡BOC = 52°

Step-by-step explanation:

Data

∡AOB = ∡COD = 25°

∡BOC = (4x + 12)°

∡AOD = 102°

Process

∡AOD = ∡AOB + ∡BOC + ∡COD

102° = 25° + 4x + 12 + 25 Solve for x

102 - 25 - 12 - 25 = 4x

4x = 40

x = 40/4

x = 10

∡BOC = 4(10) + 12

= 40 + 12

= 52°

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3 years ago

The area of the regular pentagon is 6.9 cm2. What is the perimeter? 2 cm 5 cm 10 cm 20 cm

disa [49]

Given

Area of the regular pentagon is 6.9 cm².

Find out the perimeter of a regular pentagon

To proof

Formula

Area of regular pentagon is

$= \frac{1}{4}\sqrt{5(5+2\sqrt{5})}\ a^{2}$

As given in the question

area of regular pentagon = 6.9 cm²

now equating the area value with the area formula.

$6.9 =\frac{1}{4}\sqrt{5(5+2\sqrt{5})} a^{2}$

Now put

√5 = 2.24 ( approx)

put in the above equation

$\frac{6.9\times 4}{\sqrt{5(5+2\times2.24)}}=a^{2}\\\frac{27.6}{\sqrt{47.4}}=a^{2}\\\frac{27.6}{6.88}=a^{2}$

thus

a² = 4.01

a = √ 4.01

a = 2.0 cm ( approx)

As perimeter represented the sum of all sides.

i.e regular pentagon have five sides of equal length.

Thus

perimeter of the regular pentagon = 5 × side length

= 5 ×2.00

therefore the perimeter of the regular pentagon = 10cm

option c is correct

Hence proved

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