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3 years ago

6. Andre and Clare are discussing triangle ABC that has a right angle at C and a

Mathematics

1 answer:

GalinKa [24]3 years ago

8 0

Answer:

BOTH ARE CORRECT

Step-by-step explanation:

Given that:

Triangle ABC Is right angled ;Angle ABC

Hypotenus = 15

If legs are 9 and 12 units long ;

From Pythagoras :

9² + 12² = hypotenus²

81 + 144 = 225²

2.) if:

B = 20° ; BC = will be

Using :

Cos θ = BC / 15

Cos 20 = BC / 15

BC = Cos 20 * 15

BC = 0.939692 * 15

BC = 14.09

BC = 14.1

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Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and pro

Neporo4naja [7]

${\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}$

★ Sanya has a piece of land which is in the shape of a rhombus.

★ She wants her one daughter and one son to work on the land and produce different crops, for which she divides the land in two equal parts.

★ Perimeter of land = 400 m.

★ One of the diagonal = 160 m.

${\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}$

★ Area each of them [son and daughter] will get.

${\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}$

Let, ABCD be the rhombus shaped field and each side of the field be $x$

[ All sides of the rhombus are equal, therefore we will let the each side of the field be $x$ ]

Now,

• Perimeter = 400m

$\longrightarrow \tt AB+BC+CD+AD=400m$

$\longrightarrow \tt x + x + x + x=400$

$\longrightarrow \tt 4x=400$

$\longrightarrow \tt \: x = \dfrac{400}{4}$

$\longrightarrow \tt x= \red{100m}$

$\therefore$ Each side of the field = 100m.

Now, we have to find the area each [son and daughter] will get.

So, For $\triangle$ ABD,

Here,

• a = 100 [AB]

• b = 100 [AD]

• c = 160 [BD]

$\therefore \tt Simi \: perimeter \: [S] = \boxed{ \sf \dfrac{a + b + c}{2} }$

$\longrightarrow \tt S = \dfrac{100 + 100 + 160}{2}$

$\longrightarrow \tt S = \cancel{ \dfrac{360}{2}}$

$\longrightarrow \tt S = 180m$

Using herons formula,

$\star \tt Area \: of \: \triangle = \boxed{\bf{{ \sqrt{s(s - a)(s - b)(s - c) } }}} \star$

where

• s is the simi perimeter = 180m

• a, b and c are sides of the triangle which are 100m, 100m and 160m respectively.

Putting the values,

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180(180 - 100)(180 - 100)(180 - 160) }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180(80)(80)(20) }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180 \times 80 \times 80 \times 20 }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{9 \times 20 \times 20 \times 80 \times 80}$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{ {3}^{2} \times {20}^{2} \times {80}^{2} }$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = 3 \times 20 \times 80$

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \red{ 4800 \: {m}^{2} }$

Thus, area of $\triangle$ ABD = 4800 m²

As both the triangles have same sides

So,

Area of $\triangle$ BCD = 4800 m²

Therefore, area each of them [son and daughter] will get = 4800 m²

${\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}$

★ Figure in attachment.

${\underline{\rule{290pt}{2pt}}}$

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Which of the following explains why f(x) = log4x does not have a y-intercept?

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Answer: f(x) approaches infinity

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X^2 -61 =20
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