Question

Find the length of the diagonal of a rectangle whose area is 60 cm² and width 5cm.​

Answer 1

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

◩ Diagonal = 13cm.

◩ Length = 12cm.

${\blue{\underline{\underline{\purple{\textsf{\textbf{Explanation : }}}}}}}$

Given that, A rectangle of area 60cm² and width 5cm.

To find :

• Diagonal of the rectangle.
• And it's length.

As we know that,

➡ Area of a rectangle = l × b

Here,

l (length) = x (assuming)

b (breadth) = 5cm.

Area = 60cm²

Procedure :

$\sf \longrightarrow \: {60cm}^{2} = l \times 5$

$\sf \longrightarrow \: 60 = 5l$

$\sf \longrightarrow \: l = \frac{60}{5}$

$\sf \longrightarrow \: l = 12cm$

Therefore :

➡ l (length) = 12cm.

Now,

• Using the Pythagorean theorem where taking hypotenuse as the diagonal length is perpendicular and breadth is the base.

❐ Pythagoras theorem :

$\pink{ \sf \longrightarrow \: {h}^{2} = {{p}^{2} + {b}^{2} }}$

Where,

➡ p (perpendicular) = 12 cm.

➡ b (base) = 5cm.

➡ h (hypotenuse) = ? cm.

Procedure :

$\sf \longrightarrow \: {h}^{2} = { {12}^{2} + {5}^{2} }$

$\sf \longrightarrow \: {h}^{2} = {144 + 25}$

$\sf \longrightarrow \: {h}^{2} = {169}$

$\sf \longrightarrow \: h = \sqrt{169}$

$\sf \longrightarrow \: h = 13cm.$

${\blue{\underline{\underline{\purple{\textsf{\textbf{Hence, the diagonal is 13cm and length is 12cm }}}}}}}$

Answer 2

Answer:

$\large \bold {\underline{ \underline{question}}}$

Find the length of the diagonal of a rectangle whose area is 60 cm² and width 5cm.

$\large \bold {\underline{ \underline \purple{gívєn}}}$

• αrєα σf thє rєctαnglє = 60 cm²
• wídth = 5 cm

$\large \bold { \underline {\underline \pink{sσlutíσn}}}$

❥ αrєα σf rєctαnglє = 60 cm²

$\boxed{ \bold\green{αrєα \: σf \: rєctαnglє =l \times b} }$

whєrє

l= lєnght

b= вrєαth

suвsítutє thє vαluєs ín thє αвσvє fσrmula

➥60 = l × 5

➥l= 60/5

➥l= 12 cm

______________________

$\large \bold {\underline{ \underline \purple{pчthαgσrαs \: \: thєσrєm}}}$

☆In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“

Nσw αssumє ∆ ADC

●AD²+ DC²= AC²

✏️5²+ 12²= x²

✏️25+144= x²

✏️169= x²

✏️x= √169

✏️x= 13cm

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