Question

A basketball court is a rectangle with a perimeter of 19m^2 + 2m - 10 and a width of m^2.
Find an expression for the length.

Answer 1

Given that:

• A basketball court is a rectangle.
• With a perimeter of 19 m² + 2 m - 10 and a width of m².

To Find:

• An expression for the length.

We know that:

• Perimeter of rectangle = 2(Length + Breadth)

We have:

• Perimeter = 19 m² + 2 m - 10
• Breadth = m²

Finding the length:

According to the question.

⟶ 19 m² + 2 m - 10 = 2(Length + m²)

⟶ 19 m² + 2 m - 10 = 2(Length) + 2 m²

⟶ 2(Length) = 19 m² + 2 m - 10 - 2 m²

⟶ 2(Length) = 17 m² + 2 m - 10

⟶ Length = (17 m² + 2 m - 10)/2

⟶ Length = 17/2 m² + m - 5

Hence,

• An expression for the length is 17/2 m² + m - 5.

Answer 2

Given:-

• Perimeter of Court = 19m²+2m-10

• Width of Court = m²

To Find:-

• Expression for the length of Court.

Formula Used:-

• ${\boxed{\bf{\red{Perimeter\:of\: Rectangle= 2(L+B)}}}}$

Solution:-

Using Formula,

$\sf :\implies\:Perimeter\:of\: Rectangle= 2(L+B)$

Putting Values,

$\sf :\implies\:19m^2+2m-10= 2(L+m^2)$

$\sf :\implies\:19m^2+2m-10= 2L+2m^2$

$\sf :\implies\:2L = 19m^2-2m^2+2m-10$

$\sf :\implies\:2L = 17m^2+2m-10$

$\sf :\implies\:L = \dfrac{17m^2+2m-10}{2}$

$\sf :\implies\:L = \dfrac{17m^2}{2}+\dfrac{2m}{2}-\dfrac{10}{2}$

$\bf :\implies\:L = \dfrac{17m^2}{2}+m-5$

Hence, The expression for the length of the rectangular basketball court is 17m²/2 + m - 5.

━━━━━━━━━━━━━━━━━━━━━━━━━

More Formula for Rectangle:-

• $\sf Area\:of\: Rectangle =Length \times Breadth$

• $\sf Diagonal\:of\: Rectangle =\sqrt{L^2+B^2}$

━━━━━━━━━━━━━━━━━━━━━━━━━