- perimeter=70cm
- Area=300cm^2
#1
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
#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]
