IN THE GIVEN FIGURE,AD=13 cm,BC=12 cm,AB=3cm AND ANGLE ABC=90°.FIND THE LENGTH OF DC
Answers
Answer:
Given:-
In, Δ ABC & Δ ACD
AD = 13 cm
BC = 12 cm
AB = 3 cm
ACD = ABC= 90°
To find :-
length of side DC
Solution :-
Δ ABC is a right angled triangle, with angle B measuring 90°
•°•By pythagoras theorem,
AC² = AB² + BC²
AC is the hypotenuse as according to the figure it's the side located opposite to the right angle,B. AB and BC are two remaining sides of the triangle ABC.
Plug the values of the sides,
AC² = 3² + 12²
AC² = 9 + 144
AC² = 153
AC = √153
√153 = 12.39
Therefore it's much better to leave it as it is in the form of sqaure root so that our calculation goes easy.
AC = √ 153 cm ----> 1
This AC, is the base of the Δ ACD.
Δ ACD is a right angled triangle, angle C = 90°
•°• by pythagoras theorem,
AD² = AC² + DC²
AD is the hypotenuse as according to the figure it's the side located opposite to the right angle,C. AC and DC are two remaining sides of the triangle ACD.
Plug the values of sides,
13² = (√153²) + DC²
169 = 153 + DC²
169 - 153 = DC²
16 = DC²
DC² = 16
DC = √ 16
DC = 4 cm
Length of side DC = 4cm
Just for a better explanation :-
(√153)² = √153 × √153 = 153
When a number within square root is multiplied twice which have same power and radicand, the resulting number is the number within the square root itself.