If in ∆ABC , ∠C = 90° , CD⏊AB, CD = h, BC = a, CA = b and AB = c, prove that 1/h² = 1/a² + 1/b².

Step-by-step explanation:

In ∆ ABC, ∠C = 90°, CD ⏊ AB, CD =h, BC = a, CA = b, AB = c, Prove that

Given that,

In ∆ABC, ∠C = 90° and BC = a, CA = b, AB = c

So, Area of ∆ ABC is given by

Also,

In ∆ ABC, CD ⏊ AB

So, Area of ∆ABC is given by

From equation (1) and (2), we get

Again, In right ∆ ABC

Using Pythagoras Theorem, we have

On substituting the value of c, from equation (3), we get

can be rewritten as

Hence, Proved.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

1. Pythagoras Theorem :-

This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem:

If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.