Please refer to **Case Study Chapter 10 Construction Mathematics** with answers provided below. These case study based questions are expected to come in the upcoming Class 10 Mathematics examinations. We have provided case study questions class 10 maths for all chapters on our website as per the latest examination pattern issued by CBSE, NCERT, and KVS.

**Chapter 10 Construction Case study Questions Class 10 Maths**

**I. The management of a school decided to arouse interest of their students in Mathematics. So they want to construct some geometrical shapes in one corner of the school premises. They showed a rough sketch of a right triangular structure on a plane sheet of paper with sides AB = 6 m, BC = 8 m and ∠B = 90°. The diagram shows a perpendicular from the vertex B to the front side AC. They want to build a circular wall through B, C and D but they had certain problems in doing so. So they called on some students of class X to solve this problem. They made some suggestions.**

**Question. Referring to the above, what is the length of perpendicular drawn on side AC from vertex B? **

(a) 2.6 m

(b) 3.0 m

(c) 4.8 m

(d) 4.0 m

**Answer**

C

**Question. To find centre of the circle, the students made some suggestions which are as follows: **

(a) Draw perpendicular BD on AC

(b) Draw perpendicular bisectors of BC and CD.

(c) The intersecting point of perpendiculars of BC and CD are the centre of the circle.

(d) All of the above

**Answer**

D

**Question. Referring to the above, the length of tangent AE is **

(a) 10 m

(b) 8 m

(c) 12 m

(d) 6 m

**Answer**

D

**Question. Referring to the above, what will be the length of AD? **

(a) 3.6 m

(b) 3.8 m

(c) 4.8 m

(d) 5.6 m

**Answer**

A

**Question. Referring to the above, sum of angles ∠BAE and ∠BOE is **

(a) 120°

(b) 180°

(c) 90°

(d) 60°

**Answer**

B

**II. The construction of a road is in progress. A road already exists through a forest that goes over a circular lake. The engineer wants to build another road through the forest that connects this road, but does not go through the lake.As it turns out, the road the engineer will be building and the road it will connect to both represent characteristics of a circle that have their own name. The road/bridge that already exists is called a secant of the circular lake, and the road the engineer is going to build is called the tangent of the circular lake.**

**Question. Refer to the question (2) if the road under construction, PT is 6 km and it is inclined at an angle of 30° to the line joining the centre, the radius of the lake is **

(a) 3√3 km

(b) 4√3 km

(c) 2√3 km

(d) 5√3 km

**Answer**

C

**Question. Refer to the above, if PT = 12 km and PA = 9 km, then the length of existing bridge is **

(a) 7 km

(b) 9 km

(c) 12 km

(d) 16 km

**Answer**

A

**Question. Refer to the question (3) above, the area of the lake is **

(a) 12π km^{2}

(b) 16π km^{2}

(c) 18π km^{2}

(d) 9π km^{2}

**Answer**

A

**Question. Refer to the above if the length of existing bridge is 5 km and the length of the existing road outside the lake is 4 km, then the length of the road under construction is **

(a) 4 km

(b) 6 km

(c) 10 km

(d) 14 km

**Answer**

B

**Question. Refer to the question (3) above, the circumference of the lake is **

(a) 2√3 π km

(b) 3√3 π km

(c) 4√3 π km

(d) 5√3 π km

**Answer**

C