Question

Find the perimeter of a rectangle whose length is 150m and the diagonal is 170m

Answer 1

Given :-  

• Length of the rectangle is 150 m  
• Diagonal of the rectangle is 170 m  

To Find :-  

• Perimeter of the rectangle  

Solution :-

~Here , we need to find the breadth first to find the perimeter .  

As we know that ,  

Diagonal = √ l² + b²  

By putting the values ::  

→ 170 = √150² + b²  

→ 170² = 150² + b²  

→ 28900 = 22500 + b²  

→ b² = 28900 – 22500  

→ b² = 6400  

→ b = √6400

→ b = 80 m  

Finding the perimeter ::  

→  Perimeter = 2 ( l + b )  

Where ,  

• L is the breadth  
• B is the breadth  

→ 2 ( 150 + 80 )

→ 2 ( 230 )

→ 460 m  

Therefore  

Perimeter of the rectangle is 460 m  

More Formulas :-  

Perimeter = 2 ( l + b )  

Area = lb  

Diagonal = l + b  

Answer 2

Step-by-step explanation:

★ Concept :-

✪ Here the concept of Perimeter of Rectangle has been used. As we see, that we are given the length and the diagonal of rectangle. Then firstly, we will find out the breadth of the rectangle. After that, by applying the required values in the formula of Perimeter of Rectangle we will get the answer.

Let's do it !!!

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★ Formula Used :-

$\star\;\underline{\boxed{\sf{\pink{Diagonal\ of\ Rectangle\ =\ \bf \sqrt{l^2\ +\ b^2}.}}}}$

$\star\;\underline{\boxed{\sf{\pink{Perimeter\ of\ Rectangle\ =\ \bf 2(length\ +\ breadth).}}}}$

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★ Solution :-

Given,

↷ Length of rectangle = 150m.

↷ Diagonal of rectangle = 170m.

-------------------------------------------------------------

~ For the breadth of rectangle ::

➲ We know that,

$\sf \rightarrow {Diagonal\ of\ Rectangle\ =\ \bf \sqrt{l^2\ +\ b^2}}$

⦾ By applying the values, we get :-

$\sf \rightarrow {Diagonal\ of\ Rectangle\ =\ \bf \sqrt{l^2\ +\ b^2}}$

$\sf \rightarrow {170\ =\ \bf \sqrt{150^2\ +\ b^2}}$

$\sf \rightarrow {170^2\ =\ \bf 150^2\ +\ b^2}$

$\sf \rightarrow {28900\ =\ \bf 22500\ +\ b^2}$

$\sf \rightarrow {b^2\ =\ \bf 28900\ -\ 22500}$

$\sf \rightarrow {b^2\ =\ \bf 6400}$

$\sf \rightarrow {b\ =\ \bf \sqrt{6400}}$

$\bf \rightarrow {Breadth,\ b\ =\ {\red {80m.}}}$

∴ Hence, breadth of rectangle = 80m.

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~ For the perimeter of rectangle ::

➲ We know that,

$\sf \mapsto {Perimeter\ of\ Rectangle\ =\ \bf 2(length\ +\ breadth)}$

⦾ By applying the values, we get :-

$\sf \mapsto {Perimeter\ of\ Rectangle\ =\ \bf 2(length\ +\ breadth)}$

$\sf \mapsto {Perimeter\ of\ Rectangle\ =\ \bf 2(150\ +\ 80)}$

$\sf \mapsto {Perimeter\ of\ Rectangle\ =\ \bf 2(230)}$

$\sf \mapsto {Perimeter\ of\ Rectangle\ =\ \bf 2 \times 230}$

$\bf \mapsto {Perimeter\ of\ Rectangle\ =\ {\orange {460m.}}}$

∴ Hence, perimeter of rectangle = 460m.

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★ More to know :-

➥ Properties of Rectangle :-

➴ The opposite sides are parallel and equal to each other.

➴ Each interior angle is equal to 90°.

➴ The sum of all the interior angles is equal to 360°.

➴ The diagonals bisect each other.

➴ Both the diagonals have the same length.