Question

plz givee me solution fast​

Answer 1

Answer:

It's so simple:::

2:1

Plzz mark as brainliest

Answer 2

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept}}}$

Here the Concept of Pythagoras Theorem had been used. We see we are given that the diagonal of the rectangle is thrice the smaller side. This means if we take the smaller side as x then the diagonal will be 3x . Also we know that sides of rectangle are perpendicular to its adjacent side. This means when we join diagonal, we will get Right Triangle. From that we can find the answer.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{\pink{(Hypotenuse)^{2}\;=\;\bf{(Base)^{2}\;+\;(Height)^{2}}}}}$

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★ Solution :-

Let's understand the figure first.

» Smaller sides = AD = BD

» Diagonal = AC

» Bigger sides = AB = CD

» Diagonal = 3 × Smaller Side

• Let the smaller side be x

• Let the bigger side be y

Then,

• Diagonal will be 3x

We know that, ∠ABC = 90° since uts a Rectangle. So ∆ABC is a right angled triangle. Hence Pythagoras theorem can be applied here. So,

✒ Pythagoras Theorem : In a right angled triangle, square of the longest side that is Hypotenuse is equal to the sum of squares of other two sides.

In ∆ABC,

→ Hypotenuse = AC = 3x

→ Base = AB = y

→ Height = BC = x

Then using the Pythagoras Theorem, we get

$\\\;\sf{:\rightarrow\;\;(Hypotenuse)^{2}\;=\;\bf{(Base)^{2}\;+\;(Height)^{2}}}$

By applying values,

$\\\;\sf{:\Longrightarrow\;\;(AC)^{2}\;=\;\bf{(AB)^{2}\;+\;(BC)^{2}}}$

$\\\;\sf{:\Longrightarrow\;\;(3x)^{2}\;=\;\bf{(x)^{2}\;+\;(y)^{2}}}$

$\\\;\sf{:\Longrightarrow\;\;9x^{2}\;=\;\bf{x^{2}\;+\;y^{2}}}$

$\\\;\sf{:\Longrightarrow\;\;y^{2}\;=\;\bf{9x^{2}\;-\;x^{2}}}$

$\\\;\sf{:\Longrightarrow\;\;y^{2}\;=\;\bf{8x^{2}}}$

$\\\;\sf{:\Longrightarrow\;\;y\;=\;\bf{\sqrt{8x^{2}}}}$

$\\\;\bf{:\Longrightarrow\;\;y\;=\;\bf{\orange{2\sqrt{2}\;\:x}}}$

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~ For the ratio of sides ::

$\\\;\rm{\odot\;\;Bigger\;Side\;=\;\bf{\blue{2\sqrt{2}\;\:x}}}$

$\\\;\rm{\odot\;\;Smaller\;Side\;=\;\bf{\blue{x}}}$

Now ratio is given as,

$\\\;\sf{:\mapsto\;\;Ratio\;of\;sides\;=\;\bf{\red{\dfrac{Smaller\;Side}{Bigger\;Side}}}}$

By applying values, we get

$\\\;\sf{:\mapsto\;\;Ratio\;of\;sides\;=\;\bf{\dfrac{x}{2\sqrt{2}\;\:x}}}$

Cancelling x, we get

$\\\;\sf{:\mapsto\;\;Ratio\;of\;sides\;=\;\bf{\green{\dfrac{1}{2\sqrt{2}}}}}$

$\\\;\sf{:\mapsto\;\;Ratio\;of\;sides\;=\;\bf{\green{1\;:\;2\sqrt{2}}}}$

This is the simplest form. So,

$\\\;\underline{\boxed{\tt{Ratio\;\;of\;\;sides\;=\;\bf{\purple{1\;:\;2\sqrt{2}}}}}}$

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★ More formulas and information to know about Rectangles ::

$\\\;\sf{\gray{\leadsto\;\;Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}}$

$\\\;\sf{\gray{\leadsto\;\;Perimeter\;of\;Rectangle\;=\;2(Length\;+\;Breadth)}}$

$\\\;\sf{\gray{\leadsto\;\;Diagonal\;of\;Rectangle\;=\;\sqrt{(Length^{2}\;+\;Breadth^{2})}}}$

• Opposite sides of rectangle are equal and parallel .

• Sum of adjacent angles of rectangle = 180°

• Each angle of Rectangle = 90°

• Diagonals of rectangle bisect each other at 90° .