Question

. In the given figure, AD = 13 cm, BC = 12 cm,
AB = 3 cm and angle ACD = angle ABC = 90°.
Find the length of DC.​

Answer 1

Answer:

answer is DC equals 4 cm

Answer 2

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Given:-

• In, Δ ABC & Δ ACD
• AD = 13 cm
• BC = 12 cm
• AB = 3 cm
• $\angle{ACD}$ = $\angle{ABC}$ = 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.