Question

the ground. If the ladder is shifted in such a way that it foot in
A right angled triangle is isosceles. If the square of the hypotenuse
If the sides of a triangle are 3 m, 4 m and 6 m long, determine wheill
to what height does its top reach?
length of each of its sides?
right angled triangle
Verify whether the following triplets are Pythagorean or not
(1) (8. 9. 10)
(0 (5. 7. 12)
w) (5. 12. 13)
(W) (9, 12, 15)​

Answer 1

$Let the shortest side be x</p><p></p><p>Then, Hypotenuse =2x+6 and third side =2x+6−2  </p><p></p><p>Third side =2x+4</p><p></p><p>Since, we know that</p><p></p><p> Hypotenuse2=Base2+prependicular2</p><p></p><p>Therefore,</p><p></p><p>  (2x+4)2+x2=(2x+6)2</p><p></p><p> ⇒4x2+16+16x+x2=4x2+36+24x</p><p></p><p> ⇒x2+16x−24x+16−36=0</p><p></p><p> ⇒x2−8x−20=0</p><p></p><p> ⇒x2−(10−2)x−20=0</p><p></p><p> ⇒x2−10x+2x−20=0</p><p></p><p> ⇒x(x−10)+2(x−10)=0</p><p></p><p> ⇒(x−10)(x+2)=0</p><p></p><p>⇒x−10=0            or            x+2=0</p><p></p><p>⇒x=10               or              x=−2  (not exits)</p><p></p><p>Therefore,</p><p></p><p>Shortest side x=10m</p><p></p><p>Hypotenuse  =2x+6=2×10+6=26m</p><p></p><p>Third side =2x+4=2×10+4=24m</p><p></p><p>Hence, this is the answer. </p><p></p><p>$

this is your answer dear have a good day