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3 years ago

ABCD is a rectangle ,its diagonals meet at O.If AO = 5x+1 and BO = 4x+9,find the length of the diagonals .(lengths in cm).

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

7 0

Answer:

82 cm

Step-by-step explanation:

In rectangles diagonals are equal and bisect each other

AO = BO

5x + 1 = 4x + 9

Subtract 1 from both sides

5x = 4x + 9 -1

5x = 4x + 8

Subtract 4x from both the sides

5x - 4x = 8

x = 8

AO = 5x + 1

= 5*8 +1

= 40 + 1

AO= 41 cm

Diagonal = 2*41 = 82 cm

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Step-by-step explanation:

Given coordinates of the rectangle ABCD:

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Lets first find coordinates of C

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The distance AB and CD are equal also distance AD and BC are equal, therefore

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So the coordinates of C are:

x = a, y = b

Now the diagonals:

AC = √(a-0)² + (b-0)² = √a²+b²
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Since AC = BD, we can state they are congruent

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3 years ago

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If a circle has a Diameter of 4m and a Radius of 4 units. Then what is Circumference and Area of the circle?

Fiesta28 [93]

Answer & Step-by-step explanation:

$Circumference=d\pi \\Area=r^2\pi$

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4 years ago

P³ = 1/8 please help me if anybody can .

ivanzaharov [21]

Answer:

$p= \dfrac{1}{2}$

Step-by-step explanation:

Given equation:

$p^3=\dfrac{1}{8}$

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$\implies \sqrt[3]{p^3}= \sqrt[3]{\dfrac{1}{8}}$

$\implies p= \sqrt[3]{\dfrac{1}{8}}$

$\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:$

$\implies p= \left(\dfrac{1}{8}\right)^{\frac{1}{3}}$

$\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:$

$\implies p= \dfrac{1^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

$\textsf{Apply exponent rule} \quad 1^a=1:$

$\implies p= \dfrac{1}{8^{\frac{1}{3}}}$

Rewrite 8 as 2³:

$\implies p= \dfrac{1}{(2^3)^{\frac{1}{3}}}$

$\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\implies p= \dfrac{1}{2^{(3 \cdot \frac{1}{3})}}$

Simplify:

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$\implies p= \dfrac{1}{2^{1}}$

$\implies p= \dfrac{1}{2}$

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1 year ago

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Step-by-step explanation:

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3 years ago

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WINSTONCH [101]

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${\sf{LCM\: = \:2 \:x\: 2 \:x\: 7 \:x\: 31}}\\\\{\sf{LCM \:= \:868}}\\}\\{\sf{Therefore,}}\\\\{\sf{LCM\:(14,\: 28,\: 31)\: = \:868$

${\boxed{\sf{LCM\:=\:868}}$

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2 years ago