Question

of the perimeter of a rectangular plot is 34 m and its area is 60 square meters.what is the length of each shorter side​

Answer 1

Correct question:

The perimeter of a rectangular plot is 34 m and its area is 60 square meters. What will be the shortest length of rectangular plot?

Answer:

Shorter Length of rectangular plot will be 5 m.

Solution:

We know that,

Perimeter of rectangle = 2(L + B)

→ 2(L + B) = 34

→ L + B = 34/2

→ L + B = 17

→ B = 17 - L

We also know that,

Area of rectangle = L × B

→ L × B = 60

→ L × (17 - L) = 60

→ 17L - L² - 60 = 0

→ -L² + 17L - 60 = 0

→ L² - 17L + 60 = 0

Splitting middle term, we get,

→ L = 12 and 5

As we've to find shorter length,

Shorter Length of rectangular plot = 5 m

Hence, length of rectangular plot will be 5 m.

Answer 2

Question:

The perimeter of a rectangular plot is 34 m and its area is 60 square meters. What is the length of each shorter side.

To find:

★ To find the length of the shorter side.

Answer:

$The \: length \: of \: the \: shorter \: side \: is \: \underline{\: \sf\pink{\bold{5m}}\:}$

Given:

$\star Perimeter \: of \: the \: rectangle = 34m.$

$\star Area \: of \: the \: rectangle = 60 {m}^{2} .$

Step-by-step explanation:

$\boxed{ Perimeter \: of \: the \: rectangle = 2(l + b)}$

$\implies 34 = 2(l + b)$

$\implies l + b = 17$

$\implies \: \underline{ \: b = 17 - l \: }$

$\boxed{ Area \: of \: the \: rectangle = l \times b}$

$\implies 60 = l(17 - l)$

$\implies { - l}^{2} + 17l = 60$

$\implies {l}^{2} - 17l + 60 = 0$

Now, factorization

Product :- 60 = -12 × -5

Sum :- -17 = ( -12 ) + ( -5 )

$\implies {l}^{2} - 12l - 5l + 60 = 0$

$\implies l(l - 12) - 5(l - 12) = 0$

$\implies (l - 12)(l - 5) = 0$

$\implies l - 12 = 0 \: \: or \: \: l - 5 = 0$

$\implies l = 12 \: \: or \: \: l = 5$

To find the shorter side,

$\therefore \underline{ \: \boxed{l = 5m} \: }$

$The \: length \: of \: the \: shorter \: side \: is \: \underline{\: \sf\pink{\bold{5m}}\:}$

Formula used:

$\bigstar Perimeter \: of \: the \: rectangle = 2(l + b)$

$\bigstar Area \: of \: the \: rectangle = l \times b$