Question

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Answer 1

• perimeter=70cm
• Area=300cm^2

#1

• Length=L
• Breadth=B

For perimeter.

We know

$\\ \sf\longmapsto Perimeter=2(L+B)$

$\\ \sf\longmapsto 2(L+B)=70$

$\\ \sf\longmapsto L+B=\dfrac{70}{2}=35\dots(1)$

For area

$\\ \sf\longmapsto Area=LB$

$\\ \sf\longmapsto LB=300$

#2

• L+B=35
• LB=300

#3

Putting in (a+b)^2 formula.

$\\ \sf\longmapsto (L+B)^2=L^2+B^2+2LB$

#4

• Solving quadratic equation

$\\ \sf\longmapsto 35^2=L^2+B^2+2(300)$

$\\ \sf\longmapsto 1225=L^2+B^2+600$

$\\ \sf\longmapsto L^2+B^2=625$

Put in (a-b)^2 formula

$\\ \sf\longmapsto (L-B)^2=L^2+B^2-2AB$

$\\ \sf\longmapsto (L-B)^2=625-600$

$\\ \sf\longmapsto (L-B)^2=25$

$\\ \sf\longmapsto L-B=\pm 5$

• But we shall take it positive as its dimension.

$\\ \sf\longmapsto L-B=5\dots(2)$

Adding eq(1) and eq(2)

$\\ \sf\longmapsto 2L=40$

$\\ \sf\longmapsto L=20$

Putting in eq(1)

$\\ \sf\longmapsto 20+B=35$

$\\ \sf\longmapsto B=35-20=15$

• Length=20cm
• Breadth=15cm