Question

Please someone help me with this word problem for my math class T.T

Answer 1

Perimeter:

= 58 m (approximate)

= 58.2066 or 58.21 m (exact)

Area:

= 208 m² (approximate)

= 210.0006 or 210 m² (exact)

Explanation:

Given the following dimensions of a rectangle:

length (L) =
`√(252)` meters

width (W) =
`√(175)` meters

The formula for solving the perimeter of a rectangle is:

P = 2(L + W) or 2L + 2W

The formula for solving the area of a rectangle is:

A = L × W

Approximate Forms:

In order to determine the approximate perimeter, we must determine the perfect square that is close to the given dimensions.

13² = 169

14² = 196

15² = 225

16² = 256

Among the perfect squares provided, 16² = 256 is close to 252 (inside the given radical for the length), and 13² = 169 (inside the given radical for the width). We can use these values to approximate the perimeter and the area of the rectangle.

P = 2(L + W)

P = 2(13 + 16)

P = 58 m (approximate)

A = L × W

A = 13 × 16

A = 208 m² (approximate)

Exact Forms:

L =
`√(252)` meters = 15.8745 meters

W =
`√(175)` meters = 13.2288 meters

P = 2(L + W)

P = 2(15.8745 + 13.2288)

P = 2(29.1033)

P = 58.2066 or 58.21 m

A = L × W

A = 15.8745 × 13.2288

A = 210.0006 or 210 m²