A point D is taken on the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then

A point D is taken on the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then Correct Answer AB<sup>2</sup> + CD<sup>2</sup> = AD<sup>2</sup> + BC<sup>2</sup>

According to question,
Triangles mcq solution image
In ΔABC
AB2 = AC2 + BC2 . . . . . . . (i)
ΔACD
AD2 = AC2 + CD2
AC2 = AD2 - CD2 . . . . . . . (ii)
Put the value of AC2 in equation (i)
AB2 = AD2 - CD2 + BC2
AB2 + CD2 = AD2 + BC2
Bissoy MCQ

Related Questions

The hypotenuse of a right triangle is 2 centimeters more than linger side of the triangle. The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the hypotenuse.
The hypotenuse of a right triangle is 2 centimeters more than longer side of the traiangle is 7 centimeters less than the longer side. Find the length of the hypotenuse.
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. the length of the smallest side of the triangle PQR is:
A triangle has a base x and an altitude y. A second triangle has a base twice the altitude of the first triangle, and an altitude twice the base of the first triangle. What is the area of the second triangle?
If the hypotenuse of an isosceles right triangle has length of 8 , then the area of the triangle is
∆ABC এর ক্ষেত্রে- i. যদি ∠A = B = ∠C তবে ∆ABC সমবাহু ত্রিভুজ ii. যদি ∠A, ∠B এবং ∠C, প্রত্যেকে সূক্ষ্মকোণ তবে ∆ ABC সূক্ষ্মকোণী ত্রিভুজiii. ∠A = B + C হলে ∆ABC সমকোণী ত্রিভুজনিচের কোনটি সঠিক?
ABC is an equilateral triangle. Points D, E and F are taken as the mid-point on sides AB, BC, AC respectively, so that AD = BE = CF. Then AE, BF, CD enclosed a triangle which is:
If the area of a right triangle is 6 square meters and the hypotenuse is 5 meters, what is the perimeter of the triangle?
In ∆ABC, AB=BC and AC is the hypotenuse . The value of ∠C is_______
If the legs of a right triangle is 3 and 4, then the length of hypotenuse is approximately :