Class 7 Maths Chapter 6 Question Answers - The Triangle and Its Properties

Q1. Two angles of a triangle measure 75° and 60°. What will be the measure of its third angle?
Ans:
Measures of two angles of a triangle are 75° and 60°
Sum of the measures of two angles = 75° + 60° = 135°
Using the properties of a triangle, we know that the sum of all three angles of triangle = 180°
Therefore, the measure of the third angle = 180° - 135° = 45°.

Q2. Tim wants to construct a triangle with the lengths of sides 5 cm, 4 cm, and 9 cm. Can he do it?
Ans:
The side lengths are 5 cm, 4 cm, 9 cm.
5 cm + 4 cm = 9 cm
Here the sum of the two smaller sides is equal to the third side. But as per the triangle inequality theorem, the sum of any two sides should be greater than the third side.
Hence, using the properties of the triangle we can say that Tim will not be able to construct a triangle with sides 5 cm, 4 cm, and 9 cm.

Q3. The sides of a triangle are given as 3 cm, 4 cm, and 5 cm. Calculate the perimeter of the triangle.
Ans:
Sides of the triangle are: x = 3 cm, y = 4 cm and z = 5 cm
The perimeter of the triangle is given by P = x + y + z
P = 3 + 4 + 5
P = 12 cm
Therefore, the perimeter of the given triangle is 12 cm.

Q4. The perimeter of a triangle is given as 26 feet. If two of its sides measure 7 feet and 11 feet respectively, what is the measure of the third side?
Ans:
We know that the perimeter of a triangle is the sum of all three sides. Since we know the length of 2 sides, the length of the 3rd side can be calculated using the formula,
Perimeter = side 1 + side 2 + side 3. After substituting the given values, we get,
⇒ 26 = 7 + 11 + unknown side
Therefore, the unknown side is
=26 - (7 +11) = 8 feet
∴ The third side of the given triangle measures 8 feet.

Q5. Emma is building a triangular wooden birdhouse. If two of the angles measure 45° and 63°, what is the measure of the third angle?
Ans:
We know that the sum of the angles of a triangle adds up to 180°. Therefore, the unknown angle can be calculated using the formula
Sum of interior angles of a triangle = Angle 1 + Angle 2 + Angle 3
⇒ 180° = 45° + 63° + Angle 3
⇒ Angle 3 = 180° - (45° + 63°)
Angle 3 ⇒ 72°
∴ The third angle is 72°.

Q6. The height of a triangle is 360 feet and the base is 270 feet. Find the area of the triangle.
Ans:
The height of the triangle = 360 feet and base = 270 feet
The area of a triangle is = 1/2 × Base × Height
Area of the triangle = 1/2 × 270 × 360 = 48600 feet2
∴ Area of the triangle = 48,600 feet²

Q7. Find the perimeter of a right triangle PQR having PR as the hypotenuse and with sides PQ = 4 inches, and QR = 3 inches.
Ans:
Given, PQ = 4 inches, QR = 3 inches, PR = ?
To calculate the perimeter of the triangle, we need to know all three sides.
We will calculate the length of the hypotenuse (PR) using the Pythagoras theorem.
PR² = PQ² + QR²
PR² = 4² + 3²
PR² = 16 + 9
Therefore, PR = √25 inches
PR = 5 inches.
Now, we can calculate the perimeter of the triangle.
Perimeter of triangle PQR = Sum of the three sides
= 3 + 4 + 5 = 12
Therefore, the perimeter is 12 inches.

Q8. Find the length of the missing side of a triangular-shaped road sign whose perimeter is 48 inches and the two sides are 17 inches each.
Ans:
Let the length of the missing side be b.
Given, Perimeter = 48 inches
Length of the two equal sides = 17 inches each
Perimeter of a triangle = sum of lengths of three sides
48 = 17 + 17 + b
48 = 34 + b
b = 14
Therefore, b = 14 inches

Q9. The perimeter of a rectangular wire is 297 inches. The same wire is bent into the shape of an equilateral triangle. Find the length of each of its sides.
Ans:
We know that, the perimeter of a rectangle = total length of the wire
Length of the wire used = Perimeter of the triangle formed
Perimeter of an equilateral triangle = 3 × a
297 = 3 × a
a = 99