A new ice skating rink will be approximately rectangular in shape and will have an area of 19,720 square feet. Using an equation for the perimeter P, of the skating rink in terms of its width W, what are the dimensions of the skating rink if the perimeter is 634 feet? The dimensions of the rink are ? feet by ? feet.

The dimension of the  rectangular rink is 85ft by 232ft

Given the following parameters

The formula for finding the area is:

A = lw

lw = 19,720

l = 19,720/w

If the perimeter is 634 feet

2(l+w) = 634

2(19,720/w + w) = 634

39,440/w + 2w = 634

39,440 + 2w^2 = 634w

2w^2 - 634w + 39,440 = 0

On factorizing, w=85 or w=232

Since l = 19,720/w

l = 19,720/232

l = 85

Hence the dimension of the  rectangular rink is 85ft by 232ft

Learn more on area of triangle here: link

The dimension is: 232ft by 85ft

Step-by-step explanation:

Given

Shape: Rectangle

--- Area

--- Perimeter

Required

Determine the dimension

Area is calculated as:

This gives

Perimeter is calculated as:

This gives

Divide both sides by 2

Make L the subject

Substitute 317 - W for L in

Open brackets

Rewrite as:

Expand

Factorize:

Split

Recall that:

Hence, the dimension is: 232ft by 85ft

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.