Answer:
(A)![9](https://tex.z-dn.net/?f=9)
Step-by-step explanation:
GIVEN: The sides of a quadrilateral are
and
.
TO FIND: Find the length of the shortest side of a similar quadrilateral whose area is
times as great.
SOLUTION:
let the height of smaller quadrilateral be ![h](https://tex.z-dn.net/?f=h)
As both quadrilateral are similar,
let the length of larger quadrilateral are
times of smaller.
sides of large quadrilateral are ![3x,4x,5x\text{ and }6x](https://tex.z-dn.net/?f=3x%2C4x%2C5x%5Ctext%7B%20and%20%7D6x)
height of large quadrilateral ![=h x](https://tex.z-dn.net/?f=%3Dh%20x)
Area of lager quadrilateral ![=\text{base}\times\text{height}](https://tex.z-dn.net/?f=%3D%5Ctext%7Bbase%7D%5Ctimes%5Ctext%7Bheight%7D)
![=4x\times hx=4hx^2](https://tex.z-dn.net/?f=%3D4x%5Ctimes%20hx%3D4hx%5E2)
Area of smaller quadrilateral ![=\text{base}\times\text{height}](https://tex.z-dn.net/?f=%3D%5Ctext%7Bbase%7D%5Ctimes%5Ctext%7Bheight%7D)
as the larger quadrilateral is
times as great
![\frac{4hx^2}{4h}=9](https://tex.z-dn.net/?f=%5Cfrac%7B4hx%5E2%7D%7B4h%7D%3D9)
![x^2=9](https://tex.z-dn.net/?f=x%5E2%3D9)
![x=3](https://tex.z-dn.net/?f=x%3D3)
shortest side ![=3x=3\times3=9](https://tex.z-dn.net/?f=%3D3x%3D3%5Ctimes3%3D9)
Hence the shortest side of larger quadrilateral is
, option (A) is correct.