Question

Find the length of digonal of rectangle whose length and breadth are 12 meter and 5 meter respectuvely

Answer 1

$\large \underline{\underline{\mathfrak{Answer :}}}$

• Diagonal of rectangle is 13 m

$\underline{\underline{\mathfrak{Step-By - Step - Explanation :}}}$

GiveN :

• Length of rectangle = 12 m
• Breadth of rectangle = 5 m

To FinD :

• Length of diagonal of rectangle

SolutioN :

See the attached picture for the diagram. As we're given that the length and breadth of rectangle are 12m and 5 m respectively. And we have to find out length of diagonal.

A.T.Q,

$\large \underbrace{\sf{Diagonal \: of \: rectangle}}$

In ΔABC

• length (AB) = 12 m

• Breadth (BC) = 5 m

• Diagonal (AC) = ?

So, use Pythagoras theorem as angle of the rectangle are of 90°

$\longrightarrow \sf{(AC)^2 \: = \: (AB)^2 \: + \: (BC)^2} \\ \\ \longrightarrow \sf{AC^2 \: = \: (12)^2 \: + \: (5)^2} \\ \\ \longrightarrow \sf{AC^2 \: = \: 144 \: + \: 25} \\ \\ \longrightarrow \sf{AC^2 \: = \: 169} \\ \\ \longrightarrow \sf{AC \: = \: \sqrt{169}} \\ \\ \longrightarrow \sf{AC \: = \: \pm 13} \\ \\ \underline{\boxed{\sf{Diagonal \: = \: 13 \: m}}}$

So, Diagonal of the rectangle is 13 m. Because length can never be negative.

Answer 2

Given :

• Length of diagonal is 12 m.
• Breadth of the rectangle is 5 m.

To Find :

We have to find the length of the diagonal of the rectangle.

Explanation :

We know that, When rectangle is cutted then only we can make diagonal of the recatngle.

Then, We can use Puthagoras theorm.

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

→ (Diagonal)² = (12)² + (5)²

→ (Diagonal)² = 144 + 25

→ (Diagonal)² = 169

→ Diagonal = √169

→ Diagonal = ± 13

As, Diagonal can't be negative.

So,

→ Diagonal = 13 m

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★ Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.6,2){\sf{\large{5 m}}}\put(7.7,1){\large\sf{B}}\put(9.2,0.7){\sf{\large{12 m}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

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