Question

An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters, and the length of the path is 5 meters more than the width.


Which equation can be used to find the dimensions of the playground?

0.5(x)(x + 5) = 29
0.5(x)(x + 5) = 841
x2 + (x + 5)2 = 29
x2 + (x + 5)2 = 841

Answer 1

The answer for this question is D 

Answer 2

The diagonal of rectangular patio together with two adjacent sides of patio form right triangle.

Then by the Pythagorean theorem,

$\text{Diagonal}^2=\text{(Side 1)}^2+\text{(Side 2)}^2.$

Since

• $\text{Side 1}=x\ m;$
• $\text{Side 2}=(x+5)\ m;$
• $\text{Diagonal}=29\ m,$

then

$29^2=x^2+(x+5)^2,\\ \\x^2+(x+5)^2=841.$

Answer: correct choice is D