Let a*b denote the length of the hypotenuse of a right angle triangle whose remaining two sides have length a, b. If (12*16)*k=25 then find the value of k2.

Q. Consider a right-angled triangle with length of sides a, b and c. If a = 3 cm, b = 4 cm, then find the value of hypotenuse c?

Q. Let A (h, k), B (1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which `k' can take is given by

Join BYJU'S Learning Program

Consider a right triangle with legs of length a and b and hypotenuse of length c. Of k denotes the area of the triangle then the value of (a+b) equals

The correct option is A √c2+4kk=12×a×b∴k=ab2Also c2=a2+b2∴(a+b)2=a2+b2+2ab∴(a+b)2=c2+4k∴a+b=√c2+4k

Consider a right triangle with legs of length $a$ and $b$ and hypotenuse of length $c$ . Of $k$ denotes the area of the triangle then the value of $(a + b)$ equals

The correct option is A $\sqrt{c^{2} + 4 k}$
$k = \frac{1}{2} \times a \times b$
$∴ k = \frac{a b}{2}$
Also $c^{2} = a^{2} + b^{2}$
$∴ (a + b)^{2} = a^{2} + b^{2} + 2 a b$
$∴ (a + b)^{2} = c^{2} + 4 k$
$∴ a + b = \sqrt{c^{2} + 4 k}$