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Iahhhihigo
Answered

in a rectangle LEAN, it's perimeter is 42 m and it's length is 12 m. Find the sum of its diagonals.

a. 12m
b. 15m
c. 24m
d. 30m​

Sagot :

AGboiigo

[tex] \large\underline \bold{{SOLUTION}}[/tex]

First We will find the value of the width

  • [tex]\sf{P = 2(L+W)}[/tex]
  • [tex]\sf{42 = 2(L+12)}[/tex]
  • [tex]\sf{42 = 2L+24}[/tex]
  • [tex]\sf{42-24 = 2L}[/tex]
  • [tex]\sf{18=2L}[/tex]
  • [tex]\boxed{\sf{9=L}}[/tex]

Now that We knew the width , We will use the pythagorean theorem to find the diagonal.

[tex]\longmapsto\rm{a²+b²=c²}[/tex]

[tex]\longmapsto\rm{12²+9²=c²}[/tex]

[tex]\longmapsto\rm{144+81=c²}[/tex]

[tex]\longmapsto\rm{225=c²}[/tex]

[tex]\longmapsto\boxed{\rm{15=c}}[/tex]

Notice that in a rectangle , the diagonals are equal.

[tex]\implies\sf{Diagonal_1+Diagonal_2=Sum}[/tex]

[tex]\implies\sf{15m+15m=Sum}[/tex]

[tex]\implies\sf{30m=Sum}[/tex]

[tex] \large\underline{ \bold{ANSWER}}[/tex]

  • [tex]\text{OPTION D (30m)}[/tex]

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