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This printable supports Common Core Mathematics Standard HSG-SRT.C.8

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# Applying the Pythagorean Theorem (Grade 10)

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## Applying the Pythagorean Theorem

1.
If $BC = 6 \ "m"$, and quadrilateral ABCD is a square, what is the diameter of the circle? Round the answer to two decimal places.
1. 4.25 m
2. 6.93 m
3. 8.49 m
4. Not enough information.
2.
In the figure below, AB = 10 cm, AE = 12 cm, DE = 7 cm, and CD = 5 cm. Also, $ang A, ang E$ and $ang D$ are right angles. What is the perimeter of the figure? Round the answer to one decimal place.
1. 41.6 cm
2. 45.2 cm
3. 49.6 cm
4. 53.6 cm
3.
The circle shown has a circumference of 47.1 in. What is the area of square ABCD which is inscribed in the circle? Round the answer to one decimal place.
1. Not enough information.
2. 56.3 squared inches
3. 112.4 squared inches
4. 449.4 squared inches
4.
If AC = 8 m and AB = 12 m, what is the length of $bar{CD}$, rounded to one decimal place?
1. 2.7 m
2. 5.3 m
3. 6.0 m
4. 8.0 m
5.
$Delta ABC$ is an isosceles triangle where $AB = BC$, and $BC = 2 AC$. If the length of the altitude from vertex B is 4 cm long, what is the perimeter of the triangle? Round the answer to the nearest tenth of a centimeter.
1. 2.1 cm
2. 5.2 cm
3. 9.3 cm
4. 10.3 cm
6.
In the figure below, let the intersection of the altitude from vertex B and the extension of $bar{AC}$ be point $P$ (not labeled in figure). If $BP = 5 \ "in."$, $BC = 14 \ "in"$, and $AC = 11 \ "in"$, what is the length of $bar{AB}$, rounded to the nearest tenth of an inch?
1. 4.5 in
2. 5.4 in
3. 6.9 in
4. 12.1 in
7.
In the circle shown, with center $O$, $AC = 7 \ "in."$ and $CB = 4.5 \ "in."$ (where $bar{CB}$ is not drawn). What is the length of the radius of the circle, rounded to one decimal place? Hint: an angle inscribed in a semicircle is a right angle.
1. 2.7 in.
2. 4.2 in.
3. 5.4 in.
4. 8.3 in.
8.
In the circle pictured, $O$ is the center of the circle and $bar{AD}$ is tangent to the circle. If $AD = 5 \ "cm"$ and $DO = 6.4 \ "cm"$, what is the length of the diameter of the circle, rounded to one decimal place? Hint: A line tangent to a circle is perpendicular to the radius of the circle at that point.
1. 2.4 cm
2. 4.0 cm
3. 8.0 cm
4. 16.2 cm
9.
What is the length of the diagonal of square ABCD, if the area of the inscribed circle is $30 \ "cm"^2 ?$
1. 4.4 cm
2. 8.7 cm
3. 12.4 cm
4. 13.5 cm
10.
In $Delta ABC$ the altitude from vertex $B$ intersects the opposite side at point $D$ (not shown). Point $D$ divides $bar{AC}$ into two line segments in the ratio $5:3$. If $BD = 14.7 \ "in."$ and $AB + BC = 38.2 \ "in."$, what is the length of $bar{AC}$, rounded to one decimal place?
1. 10.4 in.
2. 12.0 in.
3. 21.0 in.
4. 23.9 in.
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