Q1 : Construct a right triangle whose base is 12cm and sum of its hypotenuse and other side is 18 cm .
Answers
Step-by-step explanation:
Hypotenuse = x
Perpendicular = y
Base = 12 cm
(Hypotenuse)² = (Base)² + (Perpendicular)²
= x² = (12)² + y²
= (18 - y)² = 144 + y² (substitute eq. I)
= [(18)² + (y)² - 2(18)(y)] = 144 + y²
= 324 + y² - 36y = 144 + y²
= y² - y² - 36y = 144 - 324
= -36y = -180
= y = 5
Perpendicular = 5 cm
The Hypotenuse will be,
= x = 18 - 5
= x = 13 cm
In the triangle, we have Hypotenuse (13 cm), Base (12 cm) and Perpendicular (5 cm).
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1. Draw a base of 12 cm name it AB.
2. Using a compass/protractor draw 90° from A. (In the given attachment, compass has been used to draw the angle)
3. Extend a line from A at 90° and name the end E.
4. Take a compass with length 5 cm and draw an arc on AE.
5. Use a compass and take 13 length, place the tip on B and draw an arc on AE.
6. Arcs drawn in step 4 and 5 will intersect at a point, name it C.
7. ∆ ABC is formed with 90° at angle A.