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1. A diagonal of a square has length 8. What is the perimeter of the square?

2. Find the altitude of an equilateral triangle if each side is 10 units long

Pythagorean Theorem

1. Side^2 + Side^2 = diagonal^2

2S^2 = 8^2 Solve for S

2. 5^2 + A^2 = 10^2

Solve for A.

Did you know?

Did you know that for a square, the length of the diagonal is equal to the side length multiplied by the square root of 2? In the given scenario, if the diagonal of a square is 8 units long, we can find the side length by dividing 8 by the square root of 2. Once we know the side length, we can easily calculate the perimeter of the square by multiplying the side length by 4. Did you know that the altitude of an equilateral triangle, which is a line segment drawn from a vertex to the opposite side at a right angle, can be found using the formula: side length multiplied by the square root of 3 divided by 2? In the given case, if each side of the equilateral triangle is 10 units long, we can substitute this value into the formula to find the altitude. The altitude can be useful in various geometrical calculations and can help determine the areas of different shapes.