Question

What are the dimensions of a rectangle with an area of 12 square cm and a perimeter of 14 cm?

Answer 1

For the rectangle

Length=ℓ

Breadth=b

Area is 12 cm2

ℓb=12

Perimeter is 16 cm

2(ℓ+b)=16

ℓ+b=8

Substitute b=12ℓ from first equation

ℓ+12ℓ=8

ℓ2+12=8ℓ

ℓ2−8ℓ+12=0

Use quadratic formula (x=−b±√b2−4ac2a) to find ℓ

ℓ=−(−8)±√(−8)2−(4×1×12)2×1

ℓ=8±√162

ℓ=8±42

ℓ1=8+42=6

ℓ2=8−42

Explanation:

For the rectangle

Length=ℓ

Breadth=b

Area is 12 cm2

ℓb=12

Perimeter is 16 cm

2(ℓ+b)=16

ℓ+b=8

Substitute b=12ℓ from first equation

ℓ+12ℓ=8

ℓ2+12=8ℓ

ℓ2−8ℓ+12=0

Use quadratic formula (x=−b±√b2−4ac2a) to find ℓ

ℓ=−(−8)±√(−8)2−(4×1×12)2×1

ℓ=8±√162

ℓ=8±42

ℓ1=8+42=6

ℓ2=8−42

Answer 2

4cm length 3cm height

Explanation: