Question

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.

Answer 1

Answer:

The dimension is: 232ft by 85ft

Step-by-step explanation:

Given

Shape: Rectangle

$A = 19720$ --- Area

$P = 634$ --- Perimeter

Required

Determine the dimension

Area is calculated as:

$A = L * W$

This gives

$19720 = L * W$

Perimeter is calculated as:

$P = 2(L + W)$

This gives

$634 = 2(L + W)$

Divide both sides by 2

$317 = L + W$

Make L the subject

$L = 317 -W$

Substitute 317 - W for L in $19720 = L * W$

$19720 = (317 - W)*W$

Open brackets

$19720 = 317W - W^2$

Rewrite as:

$W^2 - 317W + 19720 = 0$

Expand

$W^2 -232W - 85W + 19720 = 0$

Factorize:

$W(W -232) - 85(W - 232)= 0$

$(W - 85) (W - 232)= 0$

Split

$W = 85\ or\ W = 232$

Recall that:

$L = 317 -W$

$L= 317 - 85\ or\ L = 317 - 232$

$L= 232\ or\ L = 85$

Hence, the dimension is: 232ft by 85ft