Question

the perimeter of a rectangle is 68m and its length is 24m. find its breadth, area and diagonal

Answer 1

Hi ,

Let l and b are length and breadth

of the rectangle ,

l = 24 m

b = ?

Perimeter = 68m

2( l + b ) = 68

l + b = 32

24 + b = 32

b = 32 - 24

b = 8 m

2 ) area ( A ) = lb

A = 24 × 8

A = 192 m²

3 ) diagonal ( d ) = √ ( l² + b² )

d = √ ( 24 )² + 8²

= √ 576 + 64

= √640

= 8√10 m

I hope this helps you.

: )

Answer 2

$\begin{gathered}\frak{Given}\begin{cases}\sf{Perimeter\;of\;the\;rectangle=\bf{68\;m}}\\\sf{Length\;of\;the\;rectangle=\bf{24\;m}}\end{cases}\end{gathered}$

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• Need to find: The breadth, area and diagonal of the rectangle.

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$\bf{\underline{\dag\frak{\;As\;we\;know\;that\;:}}}$

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$\star\;\boxed{\pink{\sf{Perimeter_{(rectangle)}=2(l+b)}}}$

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where,

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• l is the length of the rectangle and b is the breadth of the rectangle and perimeter of the rectangle is given that is 68m.

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Therefore,

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$\begin{gathered}:\implies\sf{68=2(24+b)}\\\\\\:\implies\sf{68=48+2b}\\\\\\:\implies\sf{68-48=2b}\\\\\\:\implies\sf{20=2b}\\\\\\:\implies\sf{b=\cancel{\dfrac{20}{2}}}\\\\\\:\implies{\underline{\boxed{\pink{\frak{b=10\;m}}}}}{\;\bigstar}\end{gathered}$

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${\underline{\sf{Hence,\;the\;breadth\;of\;the\;rectangle\;is\;\bf{10\;m}}.}}$

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• ★ To calculate area of rectangle formula is given by :

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$\begin{gathered}\star\;\boxed{\purple{\sf{Area_{(rectangle)}=(Length×Breadth)}}}\\\\\\:\implies\sf{Area_{(rectangle)}=(24×10)\;m^2}\\\\\\:\implies{\underline{\boxed{\pink{\frak{Area_{(rectangle)}=240\;m^2}}}}}{\;\bigstar}\end{gathered}$

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${\underline{\sf{Hence,\;the\;area\;of\;the\;rectangle\;is\;\bf{240\;m^2}}.}}$

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Now,

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$\bf{\underline{\dag\frak{\;By\;using\;formula\;:}}}$

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$\begin{gathered}\star\;\boxed{\purple{\sf{Diagonal_{(rectangle)}=\sqrt{l^2+b^2}}}}\\\\\\:\implies\sf{Diagonal_{(rectangle)}=\sqrt{(24)^2+(10)^2}}\\\\\\:\implies\sf{Diagonal_{(rectangle)}=\sqrt{576+100}}\\\\\\:\implies\sf{Diagonal_{(rectangle)}=\sqrt{676\;m}}\\\\\\:\implies{\underline{\boxed{\pink{\frak{Diagonal_{(rectangle)}=26\;m}}}}}{\;\bigstar}\end{gathered}$

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${\underline{\sf{Hence,\;the\;length\;of\;the\;diagonal\;is\;\bf{26\;m}}.}}$