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2 years ago

Find the value of x.

Mathematics

2 answers:

Marina86 [1]2 years ago

8 0

X=10 because you use Pythagorean’s theorem!

earnstyle [38]2 years ago

4 0

Answer:

x = 10

Step-by-step explanation:

Pythagorean Theorem:

6² + 8² = x²

36 + 64 = x²

100 = x²

x = √100 or 10

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lyudmila [28]

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

★ ∆ ABC is similar to ∆DEF

★ Area of triangle ABC = 64cm²

★ Area of triangle DEF = 121cm²

★ Side EF = 15.4 cm

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

★ Side BC

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

Since, ∆ ABC is similar to ∆DEF

[ Whenever two traingles are similar, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. ]

$\therefore \tt \boxed{ \tt \dfrac{area( \triangle \: ABC )}{area( \triangle \: DEF)} = { \bigg(\frac{BC}{EF} \bigg)}^{2} }$

❍ Putting the values, [Given by the question]

• Area of triangle ABC = 64cm²

• Area of triangle DEF = 121cm²

• Side EF = 15.4 cm

$\implies \tt \dfrac{64 \: {cm}^{2} }{12 \: {cm}^{2} } = { \bigg( \dfrac{BC}{15.4 \: cm} \bigg) }^{2}$

❍ By solving we get,

$\implies \tt \sqrt{\dfrac{{64 \: cm}^{2} }{ 121 \: {cm}^{2} }} = \bigg( \dfrac{BC}{15.4 \: cm} \bigg)$

$\implies \tt \sqrt{\dfrac{{(8 \: cm)}^{2} }{ {(11 \: cm)}^{2} }} = \bigg( \dfrac{BC}{15.4 \: cm} \bigg)$

$\implies \tt \dfrac{8 \: cm}{11 \: cm} = \dfrac{BC}{15.4 \: cm}$

$\implies \tt \dfrac{8 \: cm \times 15.4 \: cm}{11 \: cm} = BC$

$\implies \tt \dfrac{123.2 }{11 } cm = BC$

$\implies \tt \purple{ 11.2 \: cm} = BC$

Hence, BC = 11.2 cm.

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

★ Figure in attachment.

$\rule{280pt}{2pt}$

4 0

2 years ago

Use the distance formula to find distance between two points. Need help on this ASAP.

astra-53 [7]

Answer:

a) 20 units

b) 2 √10 units

c) 2 √17 units

Step-by-step explanation:

The distance formula is;

D = √(y2-y1)^2 + (x2-x1)^2

a) D = √(-7-9)^2 + (-7-5)^2

D = √256 + 144

D = √400

D = 20

b) D = √(10-8)^2 + (9-2)^2

D = √(2)^2 + 6^2

D = √4 + 36)

D = √40

D = 2 √10 units

c) D = √(1 + 7)^2 + (-8+10)^2

D = √(64 + 4)

D = √68

D = 2 √17 units

3 0

3 years ago