Question

17. 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 ?
(A) 40 cm
(B) 80 cm
(C) 50 cm
(D) 30 cm
(E) None of these​

Answer 1

Answer:

Option(D)

Step-by-step explanation:

As shown in the attached figure below, ABC is the triangular scenery with sides

AB = 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 have

D is the midpoint of BC.

That is,

BC = DC = 1/2 * BC

=> BC = DC = 1/2 * 80

=> BC = DC = 40 cm

Now, from the right-angled triangle ABD, we have

AB^2 = BD^2 + AD^2

=> AD^2 = AB^2 - BD^2

=> AD^2 = 50^2 - 40^2

=> AD^2 = 900

=> AD = 30 cm

Thus, the required length of the golden thread needed is 30 cm.

Hope it helps!

Answer 2

Here's the answer! hope it helps!