Question

Two quadrilaterals are similar. The length of the row longest sides of the first quadrilateral are 40in and 60in. The lengths of the three shortest sides of the second quadrilateral are 5in, 12in, and 16in. Find the unknown lengths of the sides of these two figures .

Answer 1

The sides of the first quadrilateral are 60 in, 40 in, 30 in and 12,5 in

The sides of the second quadrilateral are 24 in, 16 in, 12 in and 5 in

Explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

Arrange the sides of each quadrilateral from largest to smallest

First quadrilateral Second quadrilateral

Longest side=60 in Longest side=c in

Second side=40 in Second side=16 in

Third side= a in Third side= 12 in

Fourth side=b in Fourth side=5 in

so

`(60)/(c)=(40)/(16)=(a)/(12)=(b)/(5)`

Find the value of c

`(60)/(c)=(40)/(16)`

`c=60(16)/40`

`c=24\ in`

Find the value of a

`(40)/(16)=(a)/(12)`

`a=40(12)/16`

`a=30\ in`

Find the value of b

`(40)/(16)=(b)/(5)`

`b=40(5)/16`

`b=12.5\ in`