MATH SOLVE

6 months ago

Q:
# 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.

Accepted Solution

A:

Answer:The length of the sides are 9 units, 18 units and 11 unitsStep-by-step explanation:Letx ----> one side of the triangley ----> the longest side of the trianglez ----> the third side of the trianglewe know thatThe perimeter of triangle is equal to[tex]P=x+y+z[/tex]we have[tex]P=38\ units[/tex]so[tex]38=x+y+z[/tex] ----> equation A[tex]x=\frac{y}{2}[/tex] -----> equation B[tex]z=y-7[/tex] ----> equation Csubstitute equation B and equation C in equation A[tex]38=\frac{y}{2}+y+(y-7)[/tex] solve for y[tex]38=\frac{5}{2}y-7[/tex] [tex]\frac{5}{2}y=38+7[/tex] [tex]\frac{5}{2}y=45[/tex] [tex]y=45(2)/5[/tex][tex]y=18\ units[/tex]Find the value of x[tex]x=\frac{y}{2}[/tex] ---> [tex]x=\frac{18}{2}=9\ units[/tex]Find the value of z[tex]z=y-7[/tex] ----> [tex]z=18-7=11\ units[/tex]thereforeThe length of the sides are 9 units, 18 units and 11 units