Question

James wants to hang a 12 yards long banner from the roof of his shop. The strings are 15 yards apart from each other. James wants the top of the banner to hang 1 meter below the roof. What is the length of each string?
Note:
- The banner is hung at the center of the roof.
- Round off to one decimal place.

• A. 1.4 yd
• B. 1.6 yd
• C. 1.8 yd
• D. 1.2 yd

Answer 1

The correct option is C 1.8 yd

Let the horizontal distance between one end of the roof and the end of the banner be $x$.
Length of the roof = 15 yd
Length of the banner = 12 yd
Vertical gap between the roof and the top of the banner = 1 yd

Let AE = FB = $x$
Hence,
$2x+12=15$
$\Rightarrow 2x=3$
$\Rightarrow x=1.5$
In $\Delta ADE$,
$A{D}^2=A{E}^2+E{D}^2$ (by Pythagorean theorem)
$\Rightarrow A{D}^2={1.5}^2+1^2$ (substitute 1.5 for AE and 1 for ED)
$\Rightarrow A{D}^2=2.25+1$
$\Rightarrow A{D}^2=3.25$
$\Rightarrow AD=\sqrt{3.25}$ (evaluate the powers)
$\Rightarrow AD=1.8$ (take the positive square for each side and round off to one place after decimal)
The length of each string is 1.8 m.
Hence, the correct answer is option C.