7TH MATHS - MEASUREMENT PERIMETER OF RIGHT ANGLED TRIANGLE AND COMBINED SHAPES-1

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Class 7 Maths – Perimeter Word Problems Quiz

1. A rectangular garden is 12m long and 8m wide. A square pool of side 4m is dug exactly at one of its corners. If you walk along the outer boundary of the remaining garden, what is your total distance?

a) 40 m b) 32 m c) 48 m d) 36 m

Correct Answer: a) 40 m When you cut a square from the corner of a rectangle, the boundary shifts inward. However, the two new inward edges (4m + 4m) perfectly replace the length of the two outer edges that were removed. The perimeter remains exactly the same as the original rectangle: 2 × (12 + 8) = 40 m.

2. A right-angled triangular plot has a base of 6m and a hypotenuse of 10m. You want to secure it by wrapping a wire around the boundary 3 times. How much wire is needed?

a) 24 m b) 72 m c) 48 m d) 144 m

Correct Answer: b) 72 m First, find the missing height using Pythagoras: √(10² - 6²) = √(100 - 36) = √64 = 8m. The perimeter for one round is 6 + 8 + 10 = 24m. Since the wire wraps around 3 times: 24m × 3 = 72m.

3. An isosceles right-angled triangle has two equal sides of length 15 cm each. If its hypotenuse is approximately 21.2 cm, what is its perimeter?

a) 30 cm b) 45.2 cm c) 51.2 cm d) 60.4 cm

Correct Answer: c) 51.2 cm The perimeter is the sum of all three sides. Add the two equal sides and the hypotenuse: 15 cm + 15 cm + 21.2 cm = 51.2 cm.

4. A piece of wire in the shape of a rectangle measuring 18 cm by 12 cm is straightened and then bent to form a perfect square. What is the side length of this new square?

a) 15 cm b) 30 cm c) 60 cm d) 12 cm

Correct Answer: a) 15 cm The length of the wire is the perimeter of the rectangle: 2 × (18 + 12) = 60 cm. When formed into a square, this 60 cm wire is divided into 4 equal sides. Side of square = 60 / 4 = 15 cm.

5. A triangular park has sides in the ratio 3:4:5. If the shortest side is 15 m and the park is right-angled, what is the perimeter of the park?

a) 45 m b) 60 m c) 75 m d) 90 m

Correct Answer: b) 60 m The shortest side ratio is 3, which corresponds to 15 m (so the multiplier is 5). The other sides are 4 × 5 = 20 m, and 5 × 5 = 25 m. Perimeter = 15 + 20 + 25 = 60 m.

6. A right-angled triangle has sides 3 cm, 4 cm, and 5 cm. What is its perimeter?

a) 9 cm b) 12 cm c) 13 cm d) 14 cm

Correct Answer: b) 12 cm The perimeter of a triangle is simply the sum of its boundary lengths. 3 cm + 4 cm + 5 cm = 12 cm.

7. A combined shape has a square of side 4 cm and a rectangle of 4 cm by 2 cm joined along their 4 cm sides. What is the total perimeter of the new shape?

a) 20 cm b) 22 cm c) 24 cm d) 26 cm

Correct Answer: a) 20 cm When joined exactly along the 4 cm edge, they form a single longer rectangle. The new length is 4 cm (square) + 2 cm (rectangle) = 6 cm. The width remains 4 cm. Perimeter = 2 × (6 + 4) = 20 cm.

8. The legs (perpendicular sides) of a right-angled triangle are 5 cm and 12 cm. What is the perimeter?

a) 30 cm b) 25 cm c) 20 cm d) 19 cm

Correct Answer: a) 30 cm First find the hypotenuse using Pythagoras: √(5² + 12²) = √(25 + 144) = √169 = 13 cm. Perimeter = 5 + 12 + 13 = 30 cm.

9. A combined shape includes a rectangle of 6 cm by 3 cm and a square of 3 cm joined perfectly along their 3 cm side. What is the total perimeter?

a) 28 cm b) 30 cm c) 26 cm d) 24 cm

Correct Answer: d) 24 cm By joining them along the 3 cm edge, the length extends from 6 cm to 9 cm (6 + 3), while the width remains 3 cm. The perimeter of this new 9x3 rectangle is 2 × (9 + 3) = 24 cm.

10. A large rectangle of 10 cm by 5 cm has a 5 cm by 5 cm square removed entirely from one of its ends. What is the perimeter of the shape that is left behind?

a) 30 cm b) 25 cm c) 20 cm d) 15 cm

Correct Answer: c) 20 cm If you remove a 5x5 square from the end of a 10x5 rectangle, what is left is a smaller square measuring exactly 5 cm by 5 cm. The perimeter of this remaining square is 4 × 5 = 20 cm.