Joy111 wrote:
Attachment:
Geometry.jpg
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?
A. 125
B. 145
C. 240
D. 290
E. It cannot be determined
Let's label the three angles in
∆PQR as follows
This means we can label the angles in the
red and
blue triangles as follows
This means, the remaining angles in the
red and
blue triangles are as follows:
Since the
red and
blue triangles have the SAME three angles, they are SIMILAR triangles.
This means the ratios of their corresponding sides must be equal.
In the
blue triangle, the side BETWEEN the
circle and the
square has length
25In the
red triangle, the side BETWEEN the
circle and the
square has length
hSo one ratio is:
25/
hIn the
blue triangle, the side BETWEEN the
star and the
square has length
hIn the
red triangle, the side BETWEEN the
star and the
square has length
4So another ratio is:
h/
4Since the ratios of corresponding sides must be equal, we can write:
25/
h =
h/
4Cross multiply to get:
h² = 100Solve: h = 10 or h = -10
Since the height must be POSITIVE, we can be certain that
h = 10So the area of ∆PQR = (base)(height)/2 = (
29)(
10)/2 = 145
Answer: B
Cheers,
Brent
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