Question

3. The width of a rectangle is 5 cm and its diagonal is 13 cm. What is it's perimeter​

Answer 1

☯ Let's consider that length of the rectangle be l.

Given that,

• Width of the rectangle is 5 cm.
• And, it's diagonal is 13 cm.

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$\underline{\boldsymbol{By \ using \ Pythagoras \ Theorem\: :}}$

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$:\implies\sf \Big(l \Big)^2 + \Big(5 \Big)^2 = \Big(13 \Big)^2 \\\\\\:\implies\sf l^2 + 25 = 169 \\\\\\:\implies\sf l^2 = 169 - 25 \\\\\\:\implies\sf l^2 = 144 \\\\\\:\implies\sf l = \sqrt{144} \\\\\\:\implies{\underline{\boxed{\frak{\purple{l = 12 \ cm}}}}}\:\bigstar$

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$\therefore\;{\underline{\sf{Here, \ measure \ of \ length \ is \ {\textsf{\textbf{12 cm}}}.}}}$

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⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\star\:\boxed{\sf{\pink{Perimeter_{\:(Rectangle)} = 2( Length + Breadth)}}}$

$:\implies\sf Perimeter_{\:(Rectangle)} = 2(12 + 5) \\\\\\:\implies\sf Perimeter_{\:(Rectangle)} = 2 \times 17 \\\\\\:\implies{\underline{\boxed{\frak{\purple{Perimeter_{\:(Rectangle)} = 34 \: cm}}}}}\:\bigstar$

⠀⠀⠀

$\therefore\;{\underline{\sf{Hence, perimeter \ of \ the \ rectangle \ is \ {\textsf{\textbf{34 cm}}}.}}}$

Answer 2

Answer:

Given :-

• The width of a rectangle is 5 cm and its diagonal is 13 cm.

To Find :-

• What is the perimeter of rectangle.

Formula Used :-

✪ Perimeter = 2(Length × Breadth) ✪

Solution :-

Given :

• Width or breadth = 5 cm
• Diagonal = 13 cm

By using Phythagorus Theorem we know that,

★ (Length)² + (Breadth) = (Diagonal)² ★

Let, the length be l

According to the question by using the formula we get,

⇒ (l)² + (5)² = (13)²

⇒ (l)² + 25 = 169

⇒ (l)² = 169 - 25

⇒ (l)² = 144

⇒ l = √144

➠ l = 12 cm

Hence, the length of rectangle is 12 cm

Now, we have to find the perimeter of a rectangle,

Given :

• Length = 12 cm
• Breadth = 5 cm

According to the question by using the formula we get,

↦ Perimeter = 2(Length × Breadth)

↦ Perimeter = 2(12 + 5)

↦ Perimeter = 2(17)

↦ Perimeter = 2 × 17

➦ Perimeter = 34 cm

∴ The perimeter of a rectangle is 34 cm .