Question

O is a point on side DA of rectangle ABCD (Figure
17.26) such that ΔOBC is an isosceles triangle. If BC = 12 cm, find the measure of OD and give reasons for your answer.

Answer with steps ​

Answer 1

O is nay point inside a rectangle ABCD such that OB= 6 cm, OA=5 cm OD=8 cm.

TO find:  OC=?

In ΔAPO, Using pythagoreous theorem

OA^2=AP^2+OP^2OA2=AP2+OP2

In ΔCSO, Using pythagoreous theorem

OC^2=CS^2+OS^2OC2=CS2+OS2

Add both equation

OA^2+OC^2=AP^2+OP^2+CS^2+OS^2OA2+OC2=AP2+OP2+CS2+OS2

OA^2+OC^2=OD^2+OB^2OA2+OC2=OD2+OB2

Substitute OB= 6 cm, OA=5 cm OD=8 cm.

5^2+OC^2=6^2+8^252+OC2=62+82

25+OC^2=36+6425+OC2=36+64

OC^2=75OC2=75

OC=5\sqrt{3}OC=53 cm

Hence, The length of OC is 5\sqrt{3}53 cm

Step-by-step explanation:

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