# Example 8 | Area bounded by arcs of quarter circles

# 04 Largest Right Triangle of Given Hypotenuse

# Two particles released from the same height and reached the base at the same time

**Problem**

Particles A and B are elevated 12 meters high from a given reference base. Particle A is projected down an incline of length 20 meters at the same time particle B is let to freely fall vertically. Find the velocity of projection of particle A if both particles strikes the base at the same time.

# Geometry-related Problems

**Example**

An isosceles triangle has an altitude equal to 12 inches and a perimeter equal to 36 inches. Find the length of the base and the length of the equal sides.

# 05 - Two runners moving in opposite directions in a circular track

**Problem**

Benjie and Jerwin is running in opposite directions in a 400-meter circular track and meet each other every 35 seconds. If Benjie can complete one track in 65 seconds. How long does it take for Jerwin to run 400 meters?

# 04 - Two runners moving in the same direction in an oval track

**Problem**

Runners A and B start together in a race around a 900-ft oval track. Runner A is making a speed of 27 ft/sec and runner B at 22.5 ft/sec. How long will it take runner A to be exactly one circumference ahead of runner B.

# 03 Maximum Revenue for Tour Bus of 80 Seats

**Problem**

A tour bus has 80 seats. Experience shows that when a tour costs P28,000, all seats on the bus will be sold. For each additional P1,000 charged, however, 2 fewer seats will be sold. Find the largest possible revenue.

A. P29,000

B. P28,500

C. P28,900

D. P28,700

# Reactions of Tripod Made from Wood Planks

**Situation**

In the figure shown, each plank carries a uniform load of 100 N/m throughout its length. The supports are on the same plane.

- Find the reaction at A.

A. 900 N

B. 800 N

C. 1400 N

D. 2400 N

- Find the reaction at B.

A. 900 N

B. 800 N

C. 1400 N

D. 2400 N

- Find the reaction at C.

A. 900 N

B. 800 N

C. 1400 N

D. 2400 N

# Support Reactions of a Trapezoidal Slab with Three Points of Support

**Situation**

A reinforced concrete slab in the shape of an isosceles trapezoid weighs 3600 N/m^{2}. It is supported on the three points as shown in the figure.

- Find the reaction at A.

A. 16,848 N

B. 6,716 N

C. 13,372 N

D. 2,010 N - Find the reaction at B.

A. 16,848 N

B. 6,716 N

C. 13,372 N

D. 2,010 N - Find the reaction at C.

A. 16,848 N

B. 6,716 N

C. 13,372 N

D. 2,010 N