Carcass wrote:
What is the area of a triangle that has two sides that each have a length of 10, and whose perimeter is equal to that of a square whose area is 81?
A. 30
B. 36
C. 42
D. 48
E. 60
If a square has AREA 81, then each side of that square has length 9 (since 9 x 9 = 81)
So the PERIMETER of that square = 9 + 9 + 9 + 9 =
36The triangle that has two sides that each have a length of 10, and whose perimeter is equal to that of a square whose area is 81So the perimeter of the triangle =
36If we let x = the length of the triangle's unknown side, we can write: 10 + 10 + x =
36Solve, to get x = 16
So, the triangle has lengths 10, 10, 16 and we want to determine the area of this triangle.
Here's what we're dealing with:
Since we have an
isosceles triangle, the altitude becomes the
perpendicular bisector of the base.
As you can see, the altitude divides the triangle into
two EQUAL RIGHT trianglesSo, we can apply the Pythagorean Theorem to determine that the missing side has length
6In other words, the triangle has height
6 and base
16Area of triangle = (base)(height)/2 = (
16)(
6)/2 = 48
Answer: D
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep