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

Answer:

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

Step-by-step 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

$\frac{l}{B} =\frac{5}{8}$

l= $\frac{5B}{8}$ ........equ 2

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

$\frac{b}{B} =\frac{1}{4}$

b =$\frac{B}{4}$  ...........equ 3

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

$2*\frac{5B}{8}+\frac{B}{4}+B=100$

$\frac{5B}{4}+\frac{B}{4}+B=100$

$\frac{5B+B+4B}{4} =100$

$\frac{10B}{4} =100$

10B =400

B=40inches

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

b=$\frac{B}{4}$

b=$\frac{40}{4}$

b=10inches

l= $\frac{5B}{8}$

l= $\frac{5*40}{8}$

l=25inches