## 28 - Solved problem in maxima and minima

**Problem 28**

The perimeter of an isosceles triangle is *P* inches. Find the maximum area.

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**Problem 28**

The perimeter of an isosceles triangle is *P* inches. Find the maximum area.

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**Problem 07**

Find the area of the triangle whose vertex is at the midpoint of an upper edge of a cube of edge a and whose base coincides with the diagonally opposite edge of the cube.

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**Problem**

From the figure shown, AB = diameter of circle O_{1} = 30 cm, BC = diameter of circle O_{2} = 40 cm, and AC = diameter of circle O_{3} = 50 cm. Find the shaded areas A_{1}, A_{2}, A_{3}, and A_{4} and check that A_{1} + A_{2} + A_{3} = A_{4} as stated in the previous problem.

**Problem**

From the figure shown below, DE is the diameter of circle A and BC is the radius of circle B. If DE = 60 cm and AC = 10 cm, find the area of the shaded region.

**Solution**

**Problem**

Point P is inside the isosceles right triangle ABC. AP is 15 cm, BP is 9 cm and CP is 12 cm as shown. Determine the area of the triangle ABC.

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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.

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