Question

The width of the rectangle is 7 feet, and the diagonal length of the rectangle is 16 feet. which measurement is the closest to the length of this rectangle in feet?

a 29 ft
b 14 ft
c 17 ft
d 7 ft ​

Answer 1

b 14 ft

Explanation:

Width of the rectangle = 7 ft

Diagonal length of the rectangle = 16 ft

Let the length of the rectangle = l ft

Then,

`\[l^(2)+7^(2)=16^(2)\]`

`\[=> l^(2)+49=256\]`

`\[=> l^(2)=207\]`

`\[=> l=sqrt{207}\]`

`\[=> l=14.39\]`

This can be approximate by 14 ft

Among the given options, option B is the correct one.

Answer 2

Answer: b. 14ft

Explanation:

In the rectangle, the opposite sides are equal. The diagonal divides the rectangle into two equal right angle triangles. The diagonal represents the hypotenuse of both right angle triangles. The length and width represents the opposite and adjacent sides of the right angle triangles.

To determine the length, L of the rectangle, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

16² = L² + 7²

256 = L² + 49

L² = 256 - 49 = 207

L = √207

L = 14.38

the closest to the length of this rectangle in feet is

14ft