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Sagot :

  • perimeter=70cm
  • Area=300cm^2

#1

  • Length=L
  • Breadth=B

For perimeter.

We know

[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]

[tex]\\ \sf\longmapsto 2(L+B)=70[/tex]

[tex]\\ \sf\longmapsto L+B=\dfrac{70}{2}=35\dots(1)[/tex]

For area

[tex]\\ \sf\longmapsto Area=LB[/tex]

[tex]\\ \sf\longmapsto LB=300[/tex]

#2

  • L+B=35
  • LB=300

#3

Putting in (a+b)^2 formula.

[tex]\\ \sf\longmapsto (L+B)^2=L^2+B^2+2LB[/tex]

#4

  • Solving quadratic equation

[tex]\\ \sf\longmapsto 35^2=L^2+B^2+2(300)[/tex]

[tex]\\ \sf\longmapsto 1225=L^2+B^2+600[/tex]

[tex]\\ \sf\longmapsto L^2+B^2=625[/tex]

Put in (a-b)^2 formula

[tex]\\ \sf\longmapsto (L-B)^2=L^2+B^2-2AB[/tex]

[tex]\\ \sf\longmapsto (L-B)^2=625-600[/tex]

[tex]\\ \sf\longmapsto (L-B)^2=25[/tex]

[tex]\\ \sf\longmapsto L-B=\pm 5[/tex]

  • But we shall take it positive as its dimension.

[tex]\\ \sf\longmapsto L-B=5\dots(2)[/tex]

Adding eq(1) and eq(2)

[tex]\\ \sf\longmapsto 2L=40[/tex]

[tex]\\ \sf\longmapsto L=20[/tex]

Putting in eq(1)

[tex]\\ \sf\longmapsto 20+B=35[/tex]

[tex]\\ \sf\longmapsto B=35-20=15[/tex]

  • Length=20cm
  • Breadth=15cm
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