Question 7 - Figure it out - Page 52, 53, 54 - Chapter 2 Class 8 - The Baudhayana-Pythagoras Theorem (Ganita Part 2)

Transcript

Question 7 Construct a square whose area is equal to the difference of the areas of squares of sidelengths 5 units and 7 units.Let Side of required square = a Thus, Area of required square = a2 Given that area of square is equal to the difference of the areas of squares of sidelengths 5 units and 7 units So, we can write a2 = 72 – 52 Since we need to construct square, we don’t calculate Instead we write our equation as a2 + 52 = 72 Now, this is Pythagoras Theorem And, this is a right triangle where Sides are a, and 5. Hypotenuse is 7 So, our diagram looks like Now, making this a square Let’s construct it Now, we follow these steps First we make this right angled triangle Then we measure side a using ruler From that side a, we draw a square Let’s do this Steps of Construction 1. Draw a line segment BC of length 4 cm 2. Now, we draw 90° from point B 3. Taking C as center, 7 cm as radius, we draw an arc Let the point where arc intersects the ray be point A Join AC and label the sides Now, we measure AB = a – and then draw our square Drawing rough diagram Steps of construction 1. Draw side AB of length a 2. Now, we draw 90° from point A 3. Now, we draw 90° from point B Taking a as radius, and A as center. Draw an arc. Mark the point where arc and line intersect as D 5. Taking a as radius, and B as center. Draw an arc. Mark the point where arc and line intersect as C 6. Join CD Label the sides ∴ ABCD is the required square