5
Question 6.
The value of [5 = (-1)] lies between
Answers
Step-by-step explanation:
Base = 12 cm
Sum of Perpendicular and Hypothenuse = 18 cm
Let the hypotenuse and perpendicular be x and y respectively.
\longrightarrow⟶ x + y = 18
\longrightarrow⟶ x = 18 - y ---- (I)
Solving according to the Pythagoras theorem,
Hypotenuse = x
Perpendicular = y
Base = 12 cm
\longrightarrow⟶ (Hypotenuse)² = (Base)² + (Perpendicular)²
\longrightarrow⟶ x² = (12)² + y²
\longrightarrow⟶ (18 - y)² = 144 + y² (substitute eq. I)
\longrightarrow⟶ [(18)² + (y)² - 2(18)(y)] = 144 + y²
\longrightarrow⟶ 324 + y² - 36y = 144 + y²
\longrightarrow⟶ y² - y² - 36y = 144 - 324
\longrightarrow⟶ -36y = -180
\longrightarrow⟶ y = 5
Perpendicular = 5 cm
The Hypotenuse will be,
\longrightarrow⟶ x = 18 - 5
\longrightarrow⟶ x = 13 cm
In the triangle, we have Hypotenuse (13 cm), Base (12 cm) and Perpendicular (5 cm).
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★ Construction :
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