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1. If the length of the shorter leg of a right triangle is 5 cm and the length of the hypotenuse is 13 cm, find the length of the longer leg.

A.) 5 cm
B.) 13 cm
C.) 13 cm
D.) 12 cm

2. If a right triangle has a hypotenuse of length 15 units and a leg of length 9 units, what would be the length of the other leg?

A.) 13 units
B.) 15 units
C.) 14 units
D.) 12 units

3. In a computer catalog, the diagonal distance of a computer monitor screen is labeled as 21 inches. If the screen measures 14 inches in height, what is the width of the screen?

A.) 345 in
B.) 261 in
C.) 245 in
D.) 10 in

4. The shortest path from point A to point B goes through a pond. To avoid the pond, you must walk straight 23 meters along one edge of the pond, then take a 90-degree turn, and again walk straight 57 meters along another edge of the pond to reach point B. If you could walk through the pond, what would be the distance from point A to point B?

A.) 24 M
B.) 80 M
C.) 2720 M
D.) 3778 M

5. A boy is flying a kite. The length of the string is 61 meters and the horizontal distance between the boy and the kite is 60 meters. Assuming there is no slack in the string, find the height of the kite from the ground.

A.) 165 M
B.) 179 M
C.) 50 M
D.) 11 M

Answer :

1. The length of the longer leg is 12 cm.

**Answer:** B.) 12 cm

2. The length of the other leg is 12 units.

**Answer:** D.) 12 units

3. The width of the screen is square root of 245 inches.

**Answer:** C.) 245 in

4. The distance from point A to point B, if walking through the pond, is square root of 3778 meters.

**Answer:** D.) 3778 M

5. The height of the kite from the ground is square root of 121 meters.

**Answer:** D.) 11 M

Let's solve each problem step by step:

1. **First problem:**

Given the shorter leg a = 5 cm and hypotenuse c = 13 cm.

Using the Pythagorean theorem: a^2 + b^2 = c^2

5^2 + b^2 = 13^2

25 + b^2 = 169

b^2 = 169 - 25

b^2 = 144

b = square root of 144 = 12 cm

**Answer:** B.) 12 cm

2. **Second problem:**

Given hypotenuse c = 15 units and leg a = 9 units.

Using the Pythagorean theorem: a^2 + b^2 = c^2

9^2 + b^2 = 15^2

81 + b^2 = 225

b^2 = 225 - 81

b^2 = 144

b = square root of 144 = 12 units

**Answer:** D.) 12 units

3. **Third problem:**

Given diagonal d = 21 inches and height h = 14 inches.

Using the Pythagorean theorem: h^2 + w^2 = d^2

14^2 + w^2 = 21^2

196 + w^2 = 441

w^2 = 441 - 196

w^2 = 245

w = square root of 245

**Answer:** C.) 245 in

4. **Fourth problem:**

The shortest path is the hypotenuse of a right triangle with legs 23 meters and 57 meters.

Using the Pythagorean theorem: a^2 + b^2 = c^2

23^2 + 57^2 = c^2

529 + 3249 = c^2

3778 = c^2

c = square root of 3778

**Answer:** D.) 3778 M

5. **Fifth problem:**

Given horizontal distance d = 60 meters and string length s = 61 meters.

Using Pythagorean theorem: h^2 + d^2 = s^2

h^2 + 60^2 = 61^2

h^2 + 3600 = 3721

h^2 = 3721 - 3600

h^2 = 121

h = square root of 121

**Answer:** D.) 11 M

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