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

Answer:

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

Step-by-step 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

$x=\frac{y}{2}$ -----> equation B

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

substitute equation B and equation C in equation A

$38=\frac{y}{2}+y+(y-7)$

solve for y

$38=\frac{5}{2}y-7$

$\frac{5}{2}y=38+7$

$\frac{5}{2}y=45$

$y=45(2)/5$

$y=18\ units$

Find the value of x

$x=\frac{y}{2}$ ---> $x=\frac{18}{2}=9\ units$

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