Question
Question: In the figure, ABCD is a square of side 1 dm and \(\angle PAQ={{45}^{0}}\) . The perimeter (in dm) o...
In the figure, ABCD is a square of side 1 dm and ∠PAQ=450 . The perimeter (in dm) of the triangle PQC is.
(a) 2
(b) 1+2
(c) 22−1
(d) 1+3
Solution
Hint:For solving this question we will find the length of each side of the triangle PQC with the help of concepts of trigonometry and two algebraic identities of the whole square formula. Then, with the proper application of formulas and some concepts of geometry, we will solve for the correct answer.
Complete step-by-step answer:
Given:
We have a figure of square ABCD of side 1 dm and ∠PAQ=450 . We have to find the perimeter of ΔPQC . The figure is given below:
Now, let ∠QAD=x0 then, ∠BAP=450−x0 .
We will use the following formulae in solving this question:
tan450=1..................(1)tan(A−B)=1+tanA⋅tanBtanA−tanB...............(2)(a+b)(a−b)=a2−b2.........................(3)(a−b)2=a2+b2−2ab.........................(4)(a+b)2=a2+b2+2ab.........................(5)
Now, as ABCD is a square, so AB=BC=CD=AD=1 dm. Then,