Question

A rectangle has a circumference of 44 cm if the length and width are added to 3 cm in width to 192 cm2, specify the initial length and width?

Answer 1

Math

8th grades

Chapter: 8

Chapter Names: Triangle and Quadrangle

Code: 2

Code: 8.2.8

Answer:

K = 2 (p + l)

44cm / 2 = p + l

22cm = p + l

p = 22cm-l

L = (p + 3cm) (l + 3cm)

192cm² = (22cm-l + 3cm) (l + 3cm)

192cm² = (- l + 25cm) (l + 3cm)

192cm² = -l²-3l + 25cm l + 75cm²

-l² + 22cm l + 75cm²-192cm² = 0

-l² + 22cm l-117cm² = 0

l²-22cm l + 117cm² = 0

l₁, ₂ = - (- 22cm) +/- √ ((- 22cm) ²-4 (1) (117cm²)) / 2 (1)

= 22cm +/- √ (484cm²-468cm²) / 2

= 22cm +/- √ (16cm²) / 2

= 22cm +/- 4cm / 2

= 11cm +/- 2cm

l₁ = 11cm + 2cm

= 13cm

l₂ = 11cm-2cm

= 9cm

p₁ = 22cm-13cm

= 9cm

p₂ = 22cm-9cm

= 13cm

So the length and width of the rectangle are 9cm and 13cm or 13cm and 9cm respectively

Answer 2

Heyy mate ❤✌✌❤

Here's your Answer...

⤵️⤵️⤵️⤵️⤵️⤵️⤵️⤵️

given area of rectangle = 192 sq cm

            i.e., l×b = 192 ------------------ 1

given its perimeter is 56 cm

               2(l+b) = 56

                l+b = 28

                b = 28 - l -----------------------------2

substitute 2 in 1

then we get  l(28-l) = 192

  l² - 28l + 192 = 0

 l² -16l - 12l +192 = 0

 l(l-16) -12(l-16) = 0

l-12 = 0 or l-16 = 0

then l= 12 or 16
by substituting them in 1 we get
12 × b = 192 or  16 × b = 192

   then b = 16 or 12
hence if l=12 then b=16
                   or
if l=16 then b=12
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