Question

ABCD is a rectangle. What is the value of x? rectangle with length 63 m, width x m, and diagonal 65 m 2 meters 16 meters 63 meters 65 meters

Answer 1

Answer:  The correct option is (B) 16 meters.

Step-by-step explanation:  As shown in the attached figure, ABCD is a rectangle with length 63 m, width x m and diagonal 65 m.

We are given to find the value of x.

Since all the four angles of a rectangle are right angles, so triangle ABD will be a right-angled triangle, where

∠BAD = 90°, AB = 63 m, AD = x m and hypotenuse, BD = 65 m.

Using Pythagoras theorem, we have from triangle ABD that

$BD^2=AB^2+AD^2\\\\\Rightarrow 65^2=x^2+63^2\\\\\Rightarrow x=\sqrt{65^2-63^2}\\\\\Rightarrow x=\sqrt{4225-3969}\\\\\Rightarrow x=\sqrt{256}\\\\\Rightarrow x=16.$

Thus, the value of x is 16 meters.

Option (B) is CORRECT.

Answer 2

The correct answer is 16 meters

Hope this helped :)