7. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig. 8.17. How much paper of each shade has been used in it?
Answers
Answer:
Step-by-step explanation:
diagonal = 32 cm
Area of square = [tex]\dfrac{d^{2}}{2}[/tex]
[tex]=\dfrac{32*32}{2}\\\\=512 \ cm^{2}[/tex]
Diagonal separate the square into two equal triangles.
Area of upper triangle that is shaded black = area of lower triangle = 512/2
= 256 cm²
Isosceles triangle:
a = 6 cm ; b = 6 cm c = 8cm
[tex]s = \dfrac{a+b+c}{2}\\\\=\dfrac{6+6+8}{2}\\\\=\dfrac{20}{2}\\\\=10\\\\s-a = 10 - 6 = 4 \ cm\\\\s-b = 10-6 = 4 \ cm\\\\c - c = 10 - 8 = 2 \ cm\\\\Area = \sqrt{s*(s-a)(s-b)(s-c)}\\\\=\sqrt{10*4*4*2}\\\\=\sqrt{2 * 2 * 4 * 4 * 5}\\\\=4*2\sqrt{5}\\\\=8\sqrt{5}\\\\=8*2.24\\\\=17.92 \ cm^{2}[/tex]
Area of black shade paper = 256 + 17.92 = 273.92 cm²
Area of white shade paper = 256 cm²
Area of the isosceles triangle = s(s-a)(s-b)(s-c)
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Factorize 2x^2-5/3xy-2y^2
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I hope it helps you
Answer:
[tex]y = 0 \: .x = \frac{2}{3} y[/tex]
Step-by-step explanation:
[tex] \frac{2 {x}^{2} - 5 }{3xy - 2 {y}^{2} } [/tex]
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m∠RSU = (7x + 3)° and m∠UST = (11x − 21)°. If ∠RSU and ∠UST are complementary, what is the measure of each angle?
Answers
Step-by-step explanation:
m∠RSU + m∠UST = 90° (as complementary angles)
(7x + 3)° + (11x − 21)° =90°
18x -18° = 90°
18x = 108°
x = 6
so, m∠RSU = (7x + 3)° = 7(6)+3 = 45°
and m∠UST = (11x − 21)° = 11(6) -21 = 45°
The required measures of the angles ∠RSU and ∠UST are 31° and 23° respectively.
What is the angle?The angle can be defined as the one line inclined over another line. Also the angles are measured in radian or degrees.
The sum of the complementary angles is 90.
So,
∠RSU + ∠UST = 90
7x +3 + 11x - 21 = 90
18x - 18 = 90
18 (x - 1) = 90
x - 1 = 90 / 18
x - 1 = 5
x = 4
Required measures of the angles,|
1) m∠RSU = (7x + 3)°
m∠RSU = (7 * 4+ 3)°|
m∠RSU = 31°
2) m∠UST = (11x − 21)°.
m∠UST = (11 * 4 − 21)°
m∠UST = (44 − 21)°
m∠UST = 23°
Thus, the required measures of the angles ∠RSU and ∠UST are 31° and 23° respectively.
Learn more about Angles here:
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Find the length of the segment AB.
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Answer:
Its 5 i think? You just count how many units from point A to Point B is.
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483.62 - 218.25 = 265.37
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Hope this helps.
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Answer: An equation with an integer coefficient will NOT always have an integer solution.
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Answer:
Step-by-step explanation:
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Step-by-step explanation:
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============================================================
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Note:if you have any question please let me know.
