Question

the perimenter of an isoscleles trapezoi is 100 inches. the ratio of one leg to the bigger base is 5:8. and the ratio of the smaller base to the bigger base is 1:4. find the side lengths

Answer 1

The length of the sides are 40 inches, 10 inches, 25 inches

Explanation:

In an isosceles triangle, the legs are equal.

let the legs be represented by "l"

the smaller base be represented by "b"

bigger base be represented by "B"

Then from the question; the perimeter is 100 inches. perimeter is the sum of the length of sides that bound a shape.

2l + b +B =100 .................................equ 1

ratio of one leg to bigger base is 5:8

`(l)/(B) =(5)/(8)`

l=
`(5B)/(8)` ........equ 2

ratio of the smaller base to bigger base is 1:4

`(b)/(B) =(1)/(4)`

b =
`(B)/(4)` ...........equ 3

substitute equation 3 and 4 into 1 for "l" and "b" respectively

`2*(5B)/(8)+(B)/(4)+B=100`

`(5B)/(4)+(B)/(4)+B=100`

`(5B+B+4B)/(4) =100`

`(10B)/(4) =100`

10B =400

B=40inches

Substitute the value of B into equation 2 and 3 to get the value for l and b

b=
`(B)/(4)`

b=
`(40)/(4)`

b=10inches

l=
`(5B)/(8)`

l=
`(5*40)/(8)`

l=25inches