Question

One side of a triangle is half the longest side. The third side is

7
feet less than the longest side. The perimeter is
38
. Find all three sides.

Answer 1

The length of the sides are 9 units, 18 units and 11 units

Explanation:

Let

x ----> one side of the triangle

y ----> the longest side of the triangle

z ----> the third side of the triangle

we know that

The perimeter of triangle is equal to

`P=x+y+z`

we have

`P=38\ units`

so

`38=x+y+z` ----> equation A

`x=(y)/(2)` -----> equation B

`z=y-7` ----> equation C

substitute equation B and equation C in equation A

`38=(y)/(2)+y+(y-7)`

solve for y

`38=(5)/(2)y-7`

`(5)/(2)y=38+7`

`(5)/(2)y=45`

`y=45(2)/5`

`y=18\ units`

Find the value of x

`x=(y)/(2)` --->
`x=(18)/(2)=9\ units`

Find the value of z

`z=y-7` ---->
`z=18-7=11\ units`

therefore

The length of the sides are 9 units, 18 units and 11 units