Question

Find the perimeter of the rectangle whose length is 40 cm and diagonal is 50 cm . (Non-anonymous question )
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(4 Points)

Answer 1

✯Perimeter of rectangle= 140 cm.✯

Step-by-step explanation:

Given:

• Length of the rectangle = 40 cm
• Diagonal of rectangle = 50 cm.

To find:

• Perimeter of rectangle.

Solution:

Let the breadth of the rectangle be x cm.

• Length = 40 cm

We know that,

✯Diagonal of rectangle=√(l²+b²) ✯

${\underline{\sf{According\:to\:the\: question,}}}$

$\sf \implies \sqrt{ {40}^{2} + {x}^{2} } = 50 \\ \\ \sf \implies {40}^{2} + {x}^{2} = {50}^{2} \\ \\ \sf \implies 1600 + {x}^{2} = 2500 \\ \\ \sf \implies \: {x}^{2} = 2500 - 1600 \\ \\ \sf \implies \: {x}^{2} = 900 \\ \\ \sf \implies \: x = \sqrt{900} \\ \\ \sf \implies \: x = 30$

Therefore,

• Breadth of the rectangle = 30 cm.

We know that,

✯Perimeter of rectangle = 2(l+b) ✯

Perimeter of rectangle,

= 2(40+30) cm

= 2× 70 cm

= 140 cm

________________

★ Verification ★

• Length = 40 cm
• Breadth = 30 cm

Diagonal of rectangle = 50 cm

→ √(40²+30²) = 50

→ √ 2500 = 50

→ 50 = 50

Hence Verified !

Answer 2

$\large\blue{\tt Given :-}$

• Length of the rectangle = 40 cm
• Diagonal of the rectangle = 50 cm

$\large\orange{\tt To \: Find :-}$

• Perimeter of the rectangle

$\large\green{\tt Solution :-}$

We have,

• Length of the rectangle = 40 cm

Let,

• The breadth of the rectangle be “x”

We know that,

$\boxed{\tt Diagonal \: of \: rectangle = \sqrt{l^{2} + b^{2}}}$

Where,

• l = Length
• b = breadth

Substituting the given values of leagnth and breadth we get,

$:\implies\tt\sqrt{40^{2} + x^{2}} = 50$

$:\implies\tt 40^{2} + x^{2} = 50^{2}$

$:\implies\tt 1600 + x^{2} = 2500$

$:\implies\tt x^{2} = 2500 - 1600$

$:\implies\tt x^{2} = 900$

$:\implies\tt x = \sqrt{900}$

$:\implies\tt x = 30$

$\therefore\bf Breadth \: of \: the \: rectangle = 30 \: cm$

We need to find the perimeter of the rectangle :-

We also know that,

$\boxed{\tt Perimeter \: of \: rectangle = 2(l + b)}$

Where,

• l = Length
• b = breadth

Substituting the given values of leagnth and breadth we get,

$= \tt2(40+30)$

$= \tt2 \times 70$

$= \tt140 \: cm$

$\therefore\bf Perimeter \: of \: the \: rectangle = 140 \: cm$

$\large\red{\tt Verification :-}$

We have,

• Length of the rectangle = 40 cm
• Breadth of the rectangle = 30 cm
• Diagonal of the rectangle = 50 cm

Then,

$:\implies\tt\sqrt{40^{2}+30^{2}} = 50$

$:\implies\tt\sqrt{1600+900} = 50$

$:\implies\tt\sqrt{2500} = 50$

$:\implies\tt 50 = 50$

HENCE VERIFIED