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3 years ago

3. The trapezoid below contains a square and two right triangles. Find the perimeter of the trapezoid.

Mathematics

1 answer:

Zanzabum3 years ago

8 0

Answer:

Perimeter of trapezoid = 25.66 cm

Step-by-step explanation:

Trapezoid ABCD contains two triangles ΔABF, ΔCDE and a square with side length 4 cm.

By applying Pythagoras theorem in ΔABF,

AB² = BF² + AF²

AB² = 4² + 3²

AB = $\sqrt{16+9}$

AB = 5 cm

Similarly, By applying Pythagoras theorem in ΔCDE,

CD² = DE² + CE²

CD² = 4² + 4²

CD = $\sqrt{32}$

CD =5.66 cm

Perimeter of the given trapezoid = AB + BC + CD + AD

= 5 + 4 + 5.66 + (3 + 4 + 4)

= 25.66 cm

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ΔABC ~ ΔDEC. ∠1 and ∠2 have the same measure. Find DC and DE. (Hint: Let DC=x and AC=x+3. Use the figure shown.)

Sveta_85 [38]

DC/AC=EC/BC
x/(x+3)=10/16
10(x+3)=16x
10x+30=16x
30=6x
x=5
DC=x=5
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10/16=DE/AB, DE=y

10/16=y/10
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3 years ago

£750 is divided between Bridget, Caroline & Sarah so that Bridget gets twice as much as Caroline, and Caroline gets three ti

Sladkaya [172]

Answer: £225

Step-by-step explanation:

Let Sarah's amount be represented by x.

Since Caroline gets three times as much as Sarah, Caroline will get: 3x

Bridget gets twice as much as Caroline, therefore Bridget will get: 2 × 3x = 6x

Sarah = x

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Bridget = 6x

Total = x + 3x + 6x = 10x

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4 0

4 years ago

Translate to an algebraic expression n−1 increased by 110%

Anon25 [30]

Answer:

Part 1) The algebraic expression is equal to $1.10(n-1)$ or $1.10n-1.10$

Part 2) The algebraic expression is equal to $\frac{1.10}{n}$

Step-by-step explanation:

Part 1) Algebraic expression of (n-1) increased by 110%

we know that

110%=110/100=1.10

The algebraic expression of (n-1) increased by 110% is equal to multiply 1.10 by (n-1)

$1.10(n-1)$

Distributed

$1.10n-1.10$

Part 2) Algebraic expression of n^(-1) increased by 110%

we know that

110%=110/100=1.10

The algebraic expression of n^(-1) increased by 110% is equal to multiply 1.10 by n^(-1)

Remember that

$n^{-1}=\frac{1}{n}$

$1.10(n^{-1})=1.10\frac{1}{n}=\frac{1.10}{n}$

6 0

3 years ago