Two Buildings Are Situated on Level Ground, 65 Feet Apart $P$

Short Answer

Two buildings are situated on level ground, 65 feet apart, as shown in the figure. The building on the left is 30 feet high and the other building is 45 feet high. An expensive decorative banner is to be strung from the top edge of one building to the top edge of the other, pulled tightly so that it touches the ground at point $P$ somewhere between the two buildings. Let $x$ represent the distance from $P$ to the base of the building on the left. Find the value of $x$ that will minimize the length of the banner. How long is this banner?