Answer:
(A)[tex]9[/tex]
Step-by-step explanation:
GIVEN: The sides of a quadrilateral are [tex]3,4,5[/tex] and [tex]6[/tex].
TO FIND: Find the length of the shortest side of a similar quadrilateral whose area is [tex]9[/tex] times as great.
SOLUTION:
let the height of smaller quadrilateral be [tex]h[/tex]
As both quadrilateral are similar,
let the length of larger quadrilateral are [tex]x[/tex] times of smaller.
sides of large quadrilateral are [tex]3x,4x,5x\text{ and }6x[/tex]
height of large quadrilateral [tex]=h x[/tex]
Area of lager quadrilateral [tex]=\text{base}\times\text{height}[/tex]
[tex]=4x\times hx=4hx^2[/tex]
Area of smaller quadrilateral [tex]=\text{base}\times\text{height}[/tex]
[tex]=4h[/tex]
as the larger quadrilateral is [tex]9[/tex] times as great
[tex]\frac{4hx^2}{4h}=9[/tex]
[tex]x^2=9[/tex]
[tex]x=3[/tex]
shortest side [tex]=3x=3\times3=9[/tex]
Hence the shortest side of larger quadrilateral is [tex]9[/tex], option (A) is correct.
Answer:
(A)
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
As both quadrilateral are similar,
let the length of larger quadrilateral are times of smaller.
sides of large quadrilateral are
height of large quadrilateral
Area of lager quadrilateral
Area of smaller quadrilateral
as the larger quadrilateral is times as great
shortest side
Hence the shortest side of larger quadrilateral is , option (A) is correct.
Step-by-step explanation:
