Solve the problem.
-A rectangular plot of land has a 40-yd diagonal and an area of $768 \mathrm { yd } ^ { 2 }$ . Find the dimensions of the plot of land.
A) The plot of land is 4 yd by 192 yd.
B) The plot of land is 8 yd by 32 yd.
C) The plot of land is 8 yd by 96 yd.
D) The plot of land is 24 yd by 32 yd.

Question

Quizplus · Accepted Answer

The dimensions can be found using the Pythagorean theorem and the area of a rectangle. The area is given by $length \times width = 768$, and the diagonal forms a right triangle, so $a^2 + b^2 = 40^2$. The only pair of factors of 768 that also satisfies the Pythagorean theorem for a 40-yd diagonal is 24 and 32, making the correct dimensions 24 yd by 32 yd.

Solve the Problem 768yd2768 \mathrm { yd } ^ { 2 }768yd2

Solve the Problem $768 \mathrm { yd } ^ { 2 }$