The height of the triangle is 7 cm longer than its base. the area of the triangle is 60 cm squared. what is the base of the triangle?

Accepted Solution

Answer:8 cmStep-by-step explanation:Let x cm be the length of the base, then the length of the height is x+7 cm. Use formula for the area of the triangle:[tex]A_{triangle}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}[/tex]In your case,[tex]60=\dfrac{1}{2}\cdot x\cdot (x+7),\\ \\120=x(x+7),\\ \\x^2+7x-120=0,\\ \\D=7^2 -4\cdot 1\cdot (-120)=49+480=529,\\ \\x_{1,2}=\dfrac{-7\pm\sqrt{529}}{2\cdot 1}=\dfrac{-7\pm 23}{2}=-15,\ 8[/tex]Since the base cannot have negative length, then x=8 cm.