Question

If the diagonal of a rectangle measures 65cm and its sides are in the ratio 12:5, find the sides of the rectangle

I will mark him as the brainliest who answers first and correctly​

Answer 1

Given:

• Diagonal of a rectangle = 65 cm
• Ratio of the sides of a rectangle is 12:5.

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To find:

• Sides of the rectangle?

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Solution:

☯ Let ABCD be the rectangle and AC be the Diagonal.

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Given that,

• Ratio of the sides of a rectangle is 12:5.

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So, Let's consider the sides of rectangle are 12x and 5x.

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

• Each angles of a rectangle are of measure 90°.

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large 12x}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large 65 cm}\put(5.5,1.5){\sf\large 5x}\end{picture}$

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Now, In ∆ABC,

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$\bigstar\:{\underline{\sf{\pink{Using\; Pythagoras\; Theroem\;\::}}}}$

$:\implies\sf (AC)^2 = (AB)^2 + (BC)^2$

$:\implies\sf (65)^2 = (12x)^2 + (5x)^2$

$:\implies\sf 4225 = 144x^2 + 25x^2$

$:\implies\sf 4225 = 169x^2$

$:\implies\sf x^2 = \cancel{ \dfrac{4225}{169}}$

$:\implies\sf x^2 = 25$

$:\implies\sf \sqrt{x^2} = \sqrt{25}$

$:\implies{\underline{\boxed{\sf{\purple{x = 5}}}}}\;\bigstar$

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Therefore, Sides of Rectangle are,

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• 12x = 12 × 5 = 60 cm
• 5x = 5 × 5 = 25 cm

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$\therefore\;{\underline{\sf{Hence,\;sides\;of\;rectangle\;are\; {\textsf{\textbf{60\;cm\;and\;25\;cm}}}.}}}$

Answer 2

Question is given below -

If the diagonal of a rectangle measures 65 cm and its sides are in the ratio 12:5, find the sides of the rectangle.

Given that -

• The diagonal of a rectangle measures 65 cm.

• Its side in a ratio of 12:5

• Means (let) 1st side as 12a

• Means (let) 2nd side as 5a

To find -

• Side of rectangle.

Assumptions -

• ABHI as rectangle.

• AB as diagonal.

• 1st side as 12a

• 2nd side as 5a

Knowledge required -

• Sum of interior angles of rectangle measures 90° always.

Using concept -

• Phythagoras theorm.

Using formula -

• Phythagoras theorm = (Hypotenuse)² = (Height)² + (Base)²

We also write these as -

• Perpendicular as P.

• Base as B.

• Triangle as ∆.

• Angle as <

Solution -

• Side of rectangle = 60 cm & 25 cm.

What do the question says ?

• This question says that if the diagonal of a rectangle measures 65cm and its sides are in the ratio 12:5, find the sides of the rectangle. Means we have to find the sides.

Let's see procedure now -

• To solve this problem we have to use phythagoras theorm to find value of a. Afterwards putting the values we get 5 as the value of a. Afterthat substituting a's value in 1st and 2nd side (ratio) we get our final result easily. Side of rectangle = 60 cm and 25 cm.

Full solution -

• Finding value of a

Phythagoras theorm = (Hypotenuse)² = (Height)² + (Base)²

Phythagoras theorm = (AC)² = (AB)² + (BC)²

Where,

• AC = 65 cm.
• AB = 12a
• BC = 5a

Now, putting the values,

Phythagoras theorm = (AC)² = (AB)² + (BC)²

Phythagoras theorm = (65)² = (12a)² + (5a)²

Phythagoras theorm = 4225 = (144a)² + (25)²

Phythagoras theorm = 4225 = 169²

Phythagoras theorm = a² = 4225 / 169

Phythagoras theorm = a² = 25

Phythagoras theorm = √a = √5

Phythagoras theorm = a = 5

Hence, the value of a = 5

• Finding the sides of rectangle

1st side = 12 × 5 = 60 cm

2nd side = 5 × 5 = 25 cm

Hence, the sides are ( 60 and 25 ) cm.

More knowledge -

What is phythagoras theorm ?

It states that in a right-angled triangle, the ² of the h side = the sum of squares of the other two sides. The sides of this ∆ have been named as Perpendicular, Base and Hypotenuse.

Formula to find phythagoras theorm ?

Phythagoras theorm = (Hypotenuse)² = (Height)² + (Base)²

Diagram of triangle ( Phythagoras theorm )

See the above attachment.