Question

The sides of a quadrilateral are 3,4,5 and 6. Find the length of the shortest side of a similar quadrilateral whose area is 9 times as great.

A) 9

B) 13.5

C) 27

Answer 1

(A)

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.

Explanation:

Answer 2

(A)
`9`

Explanation:

GIVEN: The sides of a quadrilateral are
`3,4,5` and
`6`.

TO FIND: Find the length of the shortest side of a similar quadrilateral whose area is
`9` times as great.

SOLUTION:

let the height of smaller quadrilateral be
`h`

As both quadrilateral are similar,

let the length of larger quadrilateral are
`x` times of smaller.

sides of large quadrilateral are
`3x,4x,5x\text{ and }6x`

height of large quadrilateral
`=h x`

Area of lager quadrilateral
`=\text{base}*\text{height}`

`=4x* hx=4hx^2`

Area of smaller quadrilateral
`=\text{base}*\text{height}`

`=4h`

as the larger quadrilateral is
`9` times as great

`(4hx^2)/(4h)=9`

`x^2=9`

`x=3`

shortest side
`=3x=3*3=9`

Hence the shortest side of larger quadrilateral is
`9`, option (A) is correct.