Solve the problem.
-A room in the shape of a triangle has sides of length 8 yd, 10 yd, and 14 yd. If carpeting costs $12.50 a square yard and padding costs $4.25 a square yard, how much to the nearest dollar will it cost to carpet the room,
Assuming that there is no waste?
A) $627
B) $656
C) $637
D) $490

Question

Quizplus · Accepted Answer

First, we need to find the area of the triangle to determine how much carpeting and padding are needed. We can use Heron's formula, which is $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter of the triangle and $a$, $b$, and $c$ are the lengths of the sides. The semi-perimeter $s = \frac{8 + 10 + 14}{2} = 16$ yards. Thus, the area $A = \sqrt{16(16-8)(16-10)(16-14)} = \sqrt{16 \times 8 \times 6 \times 2} = \sqrt{1536} = 39.2$ square yards (rounded to one decimal place for simplicity).The cost for carpeting is $39.2 \times 12.50 = 490$ dollars, and the cost for padding is $39.2 \times 4.25 = 166.6$ dollars. Adding these together gives $490 + 166.6 = 656.6$ dollars, which rounded to the nearest dollar is $656.

Solve the Problem. -A Room in the Shape of a Triangle Has Sides