A triangular colourful scenery is made in a wall with sides 50 cm, 50 cm and 80 cm. A golden thread is to hang from the vertex so as to just reach the side 80 cm. How much length of golden thread is required ?

Answer:  The required length of the golden thread needed is 30 cm.Step-by-step explanation:  Given that a triangular colorful scenery is made in a wall with sides 50 cm, 50 cm and 80 cm. A golden thread is to hang from the vertex so as to just reach the side 80 cm. We are to find the length of the golden thread required.As shown in the attached figure below, ABC is the triangular scenery with sidesAB = AC = 50 cm and BC = 80 cm.AD is drawn perpendicular to BC, so that AD is the length of the golden thread required to reach side BC with length 80 cm from the vertex A.Now, since AD ⊥ BC and ΔABC is isosceles (AB = AC), so we must haveD is the midpoint of BC.That is,[tex]BD=DC=\dfrac{1}{2}BC=\dfrac{1}{2}\times0=40.[/tex]Now, from the right-angled triangle ABD, we have[tex]AB^2=BD^2+AD^2\\\\\Rightarrow AD^2=AB^2-BD^2\\\\\Rightarrow AD^2=50^2-40^2\\\\\Rightarrow AD^2=2500-1600\\\\\Rightarrow AD^2=900\\\\\Rightarrow AD=30.[/tex]Thus, the required length of the golden thread needed is 30 cm.